Does he have any other symptoms which might indicate cat flu?
I've seen this in cats with flu and cats who have had flu but overcome it. It may, of course, just be sleep, but it could also be a sign of blocked tear ducts.
Polly had these all her life, in both eyes. I became her slave when she was about five and she'd had flu previously. Nevertheless, she lived to be 22 and her eyesight seemed unaffected.
Personally, I'd advise a trip to the vet, even though it may only be sleep; best to be sure.