As far as I remember a year or so ago(when Mbappe interrupted what seemed to be a done deal) Perez said they wanted him for free, they weren't going to pay for it. In that case they will have a chance to do it in a year when Mbappe's contract with PSG expires. But I'm not sure he'll fit into Real's squad now...
Whether it fits or not is not seen from what has not happened, if indeed Perez wants Mbappe free, that means waiting is a good opportunity. Because by coincidence PSG still don't want to sell him even though this moment will benefit them instead of having to be in 2024. Regardless of where Mbappe is going later, so far the club that is closer to him is only Madrid and as he said Madrid was his dream club since childhood.
The truth is that Kylian Mbappe has had initial agreement with Real Madrid's president Fiorentino Perez even before the end of 2021/22 season but was surprised by Mbappe's last minute decision to remain at the Parc des Princes by renewing his contract with the French giants in a deal that made him the highest paid footballer in the world as of then.
That been said, Fiorentino Perez is a man whose interest for the player is still very much at it's peak. He still wants to bring the electrifying forward player to Santiago Bernabeu and if PSG fails to sell Mbappe to Real Madrid this summer they'll have to watch him go the Madrid next summer on a free transfer