While the following is difficult to verify, I believe there are only four distilleries in the USA making rye whiskey. Of these, only two and maybe only one sell that whiskey to private label bottlers. They are:
Wild Turkey. Wild Turkey makes its own Wild Turkey Rye and does not sell bulk whiskey. In other words, all of its production is used for its brands.
Jim Beam. Jim Beam makes its own Jim Beam Rye and Old Overholt Rye, which it also owns. Beam does not sell bulk whiskey.
Buffalo Trace. Buffalo Trace makes Sazerac Rye, probably made the Van Winkle rye, and may sell some of its rye to private bottlers.
Heaven Hill. Heaven Hill makes Rittenhouse Rye, Pikesville Rye and Stephen Foster Rye. They are in the bulk whiskey business and it is likely that any rye you see, other than the above, was made by them.
1. Because nobody likes to talk too much about the bulk whiskey business this stuff is almost impossible to verify.
2. The above covers the USA only. There is rye whiskey produced in Canada, but it would be identified as an import.
3. It's possible that Barton makes some rye. They do sell a rye under the Fleischmann's name. If I had to guess, though, I would say they don't and instead buy any rye they need from Heaven Hill.