I truly believe at this age you have to look at sleep on more of a weekly cycle than a daily one. My son is 4, and I truly believe that he only needs a nap 6 out of 7 days.
My rule for him is that he has to have quiet time, at least an hour in his room, on his bed. If he doesn't sleep, that's ok, but he has to try and at least pretend. On the days that he doesn't actually sleep, I just make sure he's in bed a tad earlier, then make sure he doesn't oversleep the next morning so he gets a good nap that next day.
I think having quiet time is good for everyone, even if they aren't sleeping. Wehn I start to see that he's sleeping on less days than not sleeping, I'll tell him that during his quiet time he can just look at books or something. But for now, I just want him to rest and rejuvenate, and most often he will fall asleep if he needs it.
I also have found that if it seems he hasn't had a lot of activity during a day that I won't try to offer him a nap until much later. So if I think he's not really that tired, I'll let him stay up until about 3pm and give him quiet time then, even if it's only 45 min or so.