Mine will purr when they are in a light doze, but it seems that when they drop off fully into sleep, and in REM cycle, they don't purr anymore.
I hope that helps.
I suppose that there are some who do purr in their sleep, much like us talking in ours.

Mine meows and cries in her sleep, but doesn't purr. I believe I read somewhere that it is something do only when they are awake.

amanda-that's kinda what I thought too. My cat snores which can sound a bit like purring...but a hell of a lot louder.
Mit-Really? Cool! I would end up giggling so much when she did it, I would wake her up.

I freaked out the first time she did it. Ever since we adopted her (nearly eight years ago), she insists on sleeping on the side of the bed I am on and the first time she did it I was almost asleep and I thought she was having a seizure! Now I just open an eye to make sure she isn't really having one and go back to sleep.

I've often tried getting video of it but I always seem to miss my chance by a few seconds.