diff --git a/mypy/checkexpr.py b/mypy/checkexpr.py
--- a/mypy/checkexpr.py
+++ b/mypy/checkexpr.py
@@ -56,7 +56,11 @@
 from mypy.util import split_module_names
 from mypy.typevars import fill_typevars
 from mypy.visitor import ExpressionVisitor
-from mypy.plugin import Plugin, MethodContext, MethodSigContext, FunctionContext
+from mypy.plugin import (
+    Plugin,
+    MethodContext, MethodSigContext,
+    FunctionContext, FunctionSigContext,
+)
 from mypy.typeops import (
     tuple_fallback, make_simplified_union, true_only, false_only, erase_to_union_or_bound,
     function_type, callable_type, try_getting_str_literals, custom_special_method,
@@ -730,12 +734,15 @@ def apply_function_plugin(self,
                               callee.arg_names, formal_arg_names,
                               callee.ret_type, formal_arg_exprs, context, self.chk))
 
-    def apply_method_signature_hook(
+    def apply_signature_hook(
             self, callee: FunctionLike, args: List[Expression],
-            arg_kinds: List[int], context: Context,
-            arg_names: Optional[Sequence[Optional[str]]], object_type: Type,
-            signature_hook: Callable[[MethodSigContext], CallableType]) -> FunctionLike:
-        """Apply a plugin hook that may infer a more precise signature for a method."""
+            arg_kinds: List[int],
+            arg_names: Optional[Sequence[Optional[str]]],
+            hook: Callable[
+                [List[List[Expression]], CallableType],
+                CallableType,
+            ]) -> FunctionLike:
+        """Helper to apply a signature hook for either a function or method"""
         if isinstance(callee, CallableType):
             num_formals = len(callee.arg_kinds)
             formal_to_actual = map_actuals_to_formals(
@@ -746,19 +753,40 @@ def apply_method_signature_hook(
             for formal, actuals in enumerate(formal_to_actual):
                 for actual in actuals:
                     formal_arg_exprs[formal].append(args[actual])
-            object_type = get_proper_type(object_type)
-            return signature_hook(
-                MethodSigContext(object_type, formal_arg_exprs, callee, context, self.chk))
+            return hook(formal_arg_exprs, callee)
         else:
             assert isinstance(callee, Overloaded)
             items = []
             for item in callee.items():
-                adjusted = self.apply_method_signature_hook(
-                    item, args, arg_kinds, context, arg_names, object_type, signature_hook)
+                adjusted = self.apply_signature_hook(
+                    item, args, arg_kinds, arg_names, hook)
                 assert isinstance(adjusted, CallableType)
                 items.append(adjusted)
             return Overloaded(items)
 
+    def apply_function_signature_hook(
+            self, callee: FunctionLike, args: List[Expression],
+            arg_kinds: List[int], context: Context,
+            arg_names: Optional[Sequence[Optional[str]]],
+            signature_hook: Callable[[FunctionSigContext], CallableType]) -> FunctionLike:
+        """Apply a plugin hook that may infer a more precise signature for a function."""
+        return self.apply_signature_hook(
+            callee, args, arg_kinds, arg_names,
+            (lambda args, sig:
+             signature_hook(FunctionSigContext(args, sig, context, self.chk))))
+
+    def apply_method_signature_hook(
+            self, callee: FunctionLike, args: List[Expression],
+            arg_kinds: List[int], context: Context,
+            arg_names: Optional[Sequence[Optional[str]]], object_type: Type,
+            signature_hook: Callable[[MethodSigContext], CallableType]) -> FunctionLike:
+        """Apply a plugin hook that may infer a more precise signature for a method."""
+        pobject_type = get_proper_type(object_type)
+        return self.apply_signature_hook(
+            callee, args, arg_kinds, arg_names,
+            (lambda args, sig:
+             signature_hook(MethodSigContext(pobject_type, args, sig, context, self.chk))))
+
     def transform_callee_type(
             self, callable_name: Optional[str], callee: Type, args: List[Expression],
             arg_kinds: List[int], context: Context,
@@ -779,13 +807,17 @@ def transform_callee_type(
         (if appropriate) before the signature is passed to check_call.
         """
         callee = get_proper_type(callee)
-        if (callable_name is not None
-                and object_type is not None
-                and isinstance(callee, FunctionLike)):
-            signature_hook = self.plugin.get_method_signature_hook(callable_name)
-            if signature_hook:
-                return self.apply_method_signature_hook(
-                    callee, args, arg_kinds, context, arg_names, object_type, signature_hook)
+        if callable_name is not None and isinstance(callee, FunctionLike):
+            if object_type is not None:
+                method_sig_hook = self.plugin.get_method_signature_hook(callable_name)
+                if method_sig_hook:
+                    return self.apply_method_signature_hook(
+                        callee, args, arg_kinds, context, arg_names, object_type, method_sig_hook)
+            else:
+                function_sig_hook = self.plugin.get_function_signature_hook(callable_name)
+                if function_sig_hook:
+                    return self.apply_function_signature_hook(
+                        callee, args, arg_kinds, context, arg_names, function_sig_hook)
 
         return callee
 
diff --git a/mypy/plugin.py b/mypy/plugin.py
--- a/mypy/plugin.py
+++ b/mypy/plugin.py
@@ -365,6 +365,16 @@ def final_iteration(self) -> bool:
         ('is_check', bool)  # Is this invocation for checking whether the config matches
     ])
 
+# A context for a function signature hook that infers a better signature for a
+# function.  Note that argument types aren't available yet.  If you need them,
+# you have to use a method hook instead.
+FunctionSigContext = NamedTuple(
+    'FunctionSigContext', [
+        ('args', List[List[Expression]]),     # Actual expressions for each formal argument
+        ('default_signature', CallableType),  # Original signature of the method
+        ('context', Context),                 # Relevant location context (e.g. for error messages)
+        ('api', CheckerPluginInterface)])
+
 # A context for a function hook that infers the return type of a function with
 # a special signature.
 #
@@ -395,7 +405,7 @@ def final_iteration(self) -> bool:
 # TODO: document ProperType in the plugin changelog/update issue.
 MethodSigContext = NamedTuple(
     'MethodSigContext', [
-        ('type', ProperType),                       # Base object type for method call
+        ('type', ProperType),                 # Base object type for method call
         ('args', List[List[Expression]]),     # Actual expressions for each formal argument
         ('default_signature', CallableType),  # Original signature of the method
         ('context', Context),                 # Relevant location context (e.g. for error messages)
@@ -407,7 +417,7 @@ def final_iteration(self) -> bool:
 # This is very similar to FunctionContext (only differences are documented).
 MethodContext = NamedTuple(
     'MethodContext', [
-        ('type', ProperType),                    # Base object type for method call
+        ('type', ProperType),              # Base object type for method call
         ('arg_types', List[List[Type]]),   # List of actual caller types for each formal argument
         # see FunctionContext for details about names and kinds
         ('arg_kinds', List[List[int]]),
@@ -421,7 +431,7 @@ def final_iteration(self) -> bool:
 # A context for an attribute type hook that infers the type of an attribute.
 AttributeContext = NamedTuple(
     'AttributeContext', [
-        ('type', ProperType),               # Type of object with attribute
+        ('type', ProperType),         # Type of object with attribute
         ('default_attr_type', Type),  # Original attribute type
         ('context', Context),         # Relevant location context (e.g. for error messages)
         ('api', CheckerPluginInterface)])
@@ -533,6 +543,22 @@ def func(x: Other[int]) -> None:
         """
         return None
 
+    def get_function_signature_hook(self, fullname: str
+                                    ) -> Optional[Callable[[FunctionSigContext], CallableType]]:
+        """Adjust the signature a function.
+
+        This method is called before type checking a function call. Plugin
+        may infer a better type for the function.
+
+            from lib import Class, do_stuff
+
+            do_stuff(42)
+            Class()
+
+        This method will be called with 'lib.do_stuff' and then with 'lib.Class'.
+        """
+        return None
+
     def get_function_hook(self, fullname: str
                           ) -> Optional[Callable[[FunctionContext], Type]]:
         """Adjust the return type of a function call.
@@ -721,6 +747,10 @@ def get_type_analyze_hook(self, fullname: str
                               ) -> Optional[Callable[[AnalyzeTypeContext], Type]]:
         return self._find_hook(lambda plugin: plugin.get_type_analyze_hook(fullname))
 
+    def get_function_signature_hook(self, fullname: str
+                                    ) -> Optional[Callable[[FunctionSigContext], CallableType]]:
+        return self._find_hook(lambda plugin: plugin.get_function_signature_hook(fullname))
+
     def get_function_hook(self, fullname: str
                           ) -> Optional[Callable[[FunctionContext], Type]]:
         return self._find_hook(lambda plugin: plugin.get_function_hook(fullname))
diff --git a/test-data/unit/plugins/function_sig_hook.py b/test-data/unit/plugins/function_sig_hook.py
new file mode 100644
--- /dev/null
+++ b/test-data/unit/plugins/function_sig_hook.py
@@ -0,0 +1,26 @@
+from mypy.plugin import CallableType, CheckerPluginInterface, FunctionSigContext, Plugin
+from mypy.types import Instance, Type
+
+class FunctionSigPlugin(Plugin):
+    def get_function_signature_hook(self, fullname):
+        if fullname == '__main__.dynamic_signature':
+            return my_hook
+        return None
+
+def _str_to_int(api: CheckerPluginInterface, typ: Type) -> Type:
+    if isinstance(typ, Instance):
+        if typ.type.fullname == 'builtins.str':
+            return api.named_generic_type('builtins.int', [])
+        elif typ.args:
+            return typ.copy_modified(args=[_str_to_int(api, t) for t in typ.args])
+
+    return typ
+
+def my_hook(ctx: FunctionSigContext) -> CallableType:
+    return ctx.default_signature.copy_modified(
+        arg_types=[_str_to_int(ctx.api, t) for t in ctx.default_signature.arg_types],
+        ret_type=_str_to_int(ctx.api, ctx.default_signature.ret_type),
+    )
+
+def plugin(version):
+    return FunctionSigPlugin

diff --git a/test-data/unit/check-custom-plugin.test b/test-data/unit/check-custom-plugin.test
--- a/test-data/unit/check-custom-plugin.test
+++ b/test-data/unit/check-custom-plugin.test
@@ -721,3 +721,12 @@ Cls().attr = "foo"  # E: Incompatible types in assignment (expression has type "
 [file mypy.ini]
 \[mypy]
 plugins=<ROOT>/test-data/unit/plugins/descriptor.py
+
+[case testFunctionSigPluginFile]
+# flags: --config-file tmp/mypy.ini
+
+def dynamic_signature(arg1: str) -> str: ...
+reveal_type(dynamic_signature(1))  # N: Revealed type is 'builtins.int'
+[file mypy.ini]
+\[mypy]
+plugins=<ROOT>/test-data/unit/plugins/function_sig_hook.py

New plugin hook: get_function_signature_hook
* Are you reporting a bug, or opening a feature request?

I am proposing a new feature: `get_function_signature_hook`
It works the same way as `get_method_signature_hook`, but for functions.

I needed this while working on `HKT` for `dry-python/returns`: https://github.com/dry-python/returns/pull/446


mypy/test/testcheck.py::TypeCheckSuite::testFunctionSigPluginFile