TBH there isn't much you can go for in a flat and with him still being so young. He can't handle small quick creatures like mice and gerbils (too rat like for you methinks also
) and hamsters are nocturnal and can be fiesty and nip lots if not handled well. He'd never see it awake during the day and at night they can make a racket.
A house rabbit is not advisable in a flat IMHO. And neither is a guinea pig as I think they both need grass and fresh air on a regular basis.
I'd go for the old staple of some goldfish to start with. OK a bit boring but he can watch them, pick things out for the tank and you can let him choose which ones. They have great goldfish varieties. Also easy to keep, clean out etc.
I used to keep everything from rabbits to hamsters, gerbils and pigeons when younger. Also had hermit crabs, found some slo worms in the wild, cats, dogs, ponies and goodness knows what else. My mother never got me my own actual pet in the house till I was 5 and was able to take care of it myself. Until then it was always something that I could watch/see but was not really anything needing handling etc.
Worth keeping in mind that usually once a child has had a pet a while they lose interest and the pet gets forgotten. Then its down to the parents to care for it and often the poor buggers don't have the greatest lives. I've seen so many rabbits etc rehomed via a friend of mine because kids wanted them then got bored and the parents could not be bothered or didn't have time to care for them properly.
I'd say to him to wait a little while, and see if he mentions it again over the next couple of weeks. If he is still keen then go for some fish, if not, let it slide and don't get a pet till a bit older.
dam that place 
