Some council websites have a bit where you can post lost/found ads for animals. I would try that before keeping him yourself. When we moved house, our eldest cat went missing. After a couple of months, we gave up hope. Some kind soul had started feeding him and gained his trust enough to grab him and take him to the vets. His microchip was out of date so we could not be traced. The person who found him posted in a few pet forums and on the council website like I mentioned. I was casually checking it one day when I saw his picture. 7 months from the day he vanished and we have him back

He was skinny and dirty (still had his old collar on too) so looked neglected. He was just lost. He must have been involved in an accident at some point as he has a limp - turns out his hip got broken and healed wonky. He is fine now though.
Basically, don't rule out that his owners aren't still missing him. Keeping him should only be an option after you've tried everything.