Threaded and asyncio API library
Your code is not complete but perhaps I've got your idea.

self.status = get_wrapper(self.status) looks slightly strange to me (while it works, sure).

I would prefer to use class decorators:

import asyncio
import functools

import aiohttp
import requests


def public(func):
    func.public = True
    return func


def sync_api(cls):
    def wrapper(func):
        @functools.wraps(func)
        def wrapped(self, *args, **kwargs):
            url, params = func(self, *args, **kwargs)
            response = requests.get(url, params)
            _json = response.json()
            return self.process_response(_json)

    for name in dir(cls):
        func = getattr(cls, name)
        if getattr(func, 'public'):
            setattr(cls, name, wrapper(func))


def async_api(cls):
    def wrapper(func):
        @functools.wraps(func)
        @asyncio.coroutine
        def wrapped(self, *args, **kwargs):
            url, params = func(self, *args, **kwargs)
            session = self.session
            try:
                resp = yield from session.get(url, params=params)
            except Exception as ex:
                logger.exception(ex)
                raise
            try:
                _json = yield from resp.json()
                yield from resp.release()
            except Exception as ex:
                logger.exception(ex)
                resp.close()
                raise
            else:
                return self.process_response(_json)

    for name in dir(cls):
        func = getattr(cls, name)
        if getattr(func, 'public'):
            setattr(cls, name, wrapper(func))


class BaseApi:

    @public
    def status(self):
        return 'http://example.com', {}


@sync_api
class ThreadedApi(BaseApi):
    pass


@async_api
class AsyncApi(BaseApi):

    def __init__(self):
        self.session = aiohttp.Session()


P.S. Please keep in mind that yield from resp.json() may raise an exception too.

P.P.S.
If you are using Python 3.4 I strongly suggest upgrading to 3.5.

Otherwise please use famous async def/await syntax. 
async with session.get() could simplify the snippet a little.