Are there known functions of AST, ALT, and amylase in the blood?
These enzymes, while useful markers of disease, are not only produced during the disease state, and are not only produced in one organ. It is therefore not surprising that there are always low levels released into the biochemical milieu that is the blood. If there are not even low levels of the enzymes then that might indicate that the organ is not doing it's job properly.

I'll approach this from a veterinary viewpoint but I imagine it is much the same in humans. My preferred source for information about veterinary clinical pathology is Cornell's EClinpath site.

The major tissue sources of AST are liver, skeletal muscle, and cardiac muscle. A small amount is produced by erythrocytes. In lesser concentrations it is also found in renal epithelial cells and brain tissue. It therefore should be no surprise that low levels are found in blood. It is not difficult to picture a small amount of leakage from erythrocytes in the normal state, even without pathologic haemolysis, given the regular turnover of cells and permeability of erythrocytes – although I suspect this is a minor source. Just due to the fact that the liver's normal function is to deal with many cytotoxic compounds, even in the completely healthy patient there always is going to be some low level of hepatocellular damage. As a result, a very low serum level of AST might be indicative of a poorly functioning liver (e.g. with a chronic hepatitis).

Among veterinary species there is considerable variation in the clinical usefulness of ALT. For example, it is a very useful indicator of liver disease in dogs and cats, much less so in horses. Much like AST, ALT is also produced in liver, muscle, kidney, and erythrocytes.

Amylase is known to be produced by cells in the pancreas, salivary gland, duodenum, ileum, ovary, and testes. Of course, the pancreas produces the most of this enzyme, which is why it is somewhat clinically useful (though I can't say I like it much at least for veterinary species).

The bottom line is that these enzymes play an important role in biochemical reactions of many different tissues. While the enzymes may be produced in predominance in one tissue, they have the same function (at a biochemical level) in all these tissues (i.e. they convert the same reactions). I view it more as a difference of the tissue need for these enzymes rather than a difference in function between tissues.