First of all, I do not believe in "burnout." I do not believe that a significant number of kids give up baseball because they just have too much of it.
I do believe that as kids mature, they can develop other interests. They can also get to a point where they realize they enjoy the game recreationally but not competitively. Maybe he wants to continue playing 2-3 times/week but not every day of his life. That's not burnout. That someone maturing enough to realize what he wants out of life, and that to get what he wants most, some other things may have to be let go.
Ultimately if that's where your son is, you should respect his decision.
But I would encourage him not to make this decision rashly. At his age things get very competitive and once he steps off the path it'll be darned near impossible to get back on it. I would suggest he could try a year of freshman or JV ball and see how he likes it at the end of 3 months.
Maybe it's just anxiety talking. Maybe he's nervous about tryouts. If so, then a successful season might cure that and let him discover he still enjoys playing, even every day.
But talk it through. If he thinks he's done, or if he just wants to play teenage rec ball or some such, in the end you have to respect that decision. Just make sure he doesn't put himself in the position where, two years from now, he's asking himself "what if?"