There’s domesticated, and there’s tame.
I think the vast majority of animals kept as pets (aside from cats / dogs / pot bellied pigs) are tame, rather than domesticated. Farm animals (sheep, horses, cows etc.) are presumably similarly domesticated, if not to the point of adoring us hoomans and wanting to be close to us.
A tamed animal (e.g. the budgie a few feet away from my desk; though it’s arguable whether he’s been tamed!) can learn to tolerate and possibly even enjoy human companionship, but there’s not the same level of dependence.
To choose something to be domesticated, I’d have to think of what it would be used for. Food (cows/sheep/chickens)? pets (dogs/cats)? Work (horses, elephants, dogs)? Something else?
A big cat has some appeal - but would be useless for any kind of labor. Nor do predators make good eating, I gather. Possibly as a hunting companion, as dogs have been, though that’s less useful these days. And they’re a bit too large to be practical simply as pets. There would need to be many generations of selective breeding to eliminate the worst of the predator instincts, as well, or Fluffy might wind up eating the dog (or the baby).
A potential food animal that required less resources than, say, cattle, would be a good candidate. Someone upthread mentioned deer as one possibility.
The silver fox domestication experiment is fascinating reading. I don’t know if the foxes are as thoroughly human-oriented as a dog is, but they seem to be on their way.
My personal candidate would be some kind of bird. There are numerous species of parrots kept as pets, but I do think they are tame, versus domesticated. A few generations of very selective breeding might well bring them closer to that line. Imagine a bird that genuinely loves people, has at least some of its destructive tendencies bred out, and can talk (either via simple mimicry, or even some basic conversation).