Conventional prehistory says there used to be animals we could interbreed with, but that we in fact bred with them so much that the hybrids replaced the creatures made to get said hybrid.

These replaced peoples were, of course, designated members of the homo genus, which Homo Sapiens (the scientific name for humans) gets its name from, and they include things such as (using their common names, not their scientific names) Neanderthals (geographically found in Southern Europe), Denisovans (found mostly to the West, towards Asia), and Hobbits (yes, hobbits, they were found in the Pacific). Nothing of note happened in America.

The Neanderthals and the Denisovans are of particular note, as their territories overlapped commonly, and there are cave findings that show they themselves interbred with each other and produced perfectly functioning offspring. I can only hope when they were engaging in the act, they asked to mingle and ended it with "no homo".

There are, however, reports that, at the same time in prehistory, we did try to breed with other animals that haven't been replaced, typically the great apes, as evidenced by lice samples found in both us and them, but that this, quite expectedly, didn't lead to any hybrid outcomes.