I would ABSOLUTELY knock and the people's door and ask if this is their cat. I bet they'll either say no, they don't know where he came from. Then I'd take him to the vet as soon as possible, and work on a home for him.


They might say yes, but he's outdoor only or something.

I don't think anyone would object to a friendly inquiry about the cat. If they say it's their cat, you can just say that you've noticed and wondered about him many times, and maybe ask it's name, so that you will at least know what to call it when you see it. You know, say "Hi, Bob-cat!" Nothing offensive yet, right? You can explain you're a "pet-person" and like to know the neighborhood animals.

Then, if you are comfortable with the tenor of the conversation, you can ask if he's sick ... you've noticed his fur doesn't look "right" and as a cat person, you know how fastidious cats are about their coat ...

And if (worst case scenario) they are abrupt and rude and say the cat is theirs but think everything's fine with it, I would see if the cat seems better off in a few days (now that they know someone's noticed), and if not, well, if he keeps showing up at your house, I'd feed him, and when he starts hanging out at your place all the time, I'd then consider that the cat has made the choice, vet him and find him a home.

Just me ...