Why is my cat sleeping next to the litter tray all the time?

[CloserToFiftyThanTwenty]

Just that really! Old boy, recently become an indoor cat. He shares the litter tray with our other old boy but he is definitely the alpha cat in the house.

Anyway, he spends 95% of his time asleep, and has started to sleep right next to the litter tray. As on on the mat, hanging over the edge of the tray (whether it's clean or not !). He clearly isn't bothered by his unsanitary sleeping arrangements, but should I be? Why is he doing this?

How bizarre. Cats do seem to change their sleeping arrangements fairly regularly. It's probably just a phase. If nothing else seems strange then I wouldn't worry.

It is odd - maybe guarding behaviour if he's recently become an indoor cat and is having to use just the litter tray?

I'd get another one for them to dilute the angst a little. You should really have more than the one if they're both using it, even if you clean that one meticulously.

How is his peeing? Does he ever appear to be caught short? (Just thinking that if his bladder is weakening for some reason, he might feel more secure if he's close by the tray.)

PS - how old are they both ? And was there any particular reason for him becoming an indoor cat?

Definitely get another litter tray - or even 2!
I suspect your alpha male chap is bullying the other cat by limiting availability of access to litter tray. As our boys got older one of ours started to do this and we hadn't realised what a negative effect it had on the other cat until bully cat died.