I think he might stay in PSG because the money is just too good to be avoided. But a player like him will surely be interested to play for a team like Real Madrid. and I really hope that he will play for Real Madrid because he is not going to be achieving too many things with PSG in the future in my opinion.
He isn't a new player in PSG, and Real Madrid is a rich club as well. So, I believe money won't be his reason to stay or move. He must consider playing at a bigger club where he can have the opportunity to get more prestigious trophies. Especially to get the UCL trophy that he never got in PSG. And Real Madrid is a perfect club if he considers getting more trophies, including UCL trophy as well. Since this opportunity may not come twice, I assume Mbappe will agree with the offer from Real Madrid.