I don't think winning the champion's league is the reason Mbappe is deciding to join Real Madrid, I strongly doubt that.
Real Madrid is the number one club when it comes to Champions League, no club like it, it is the Champion. I see no reason a football player wants to join Real Madrid than to be part of he teams that win Champions League we take it or leave it, it is part of his ambition and he is playing excellently.
I think in the next two years, PSG will be able to win the UEFA Champion's League and Mbappe is pretty very young so his motivation could be playing for a bigger club in Europe with rich history and heritage.
Let us hope so, but PSG has been so unlucky about Champions League, with their squared this season, it did not go as far as I thought it could go, but it was defeated by Real Madrid which will play this season final with Liverpool, so I think it is worth it. It is very possible Mbappe join Real Madrid by the end of Champions League final.