Florentino Pérez said they plan to sign Mbappe for the next season. But considering the current situation of Mbappe, I assume Pérez may try to sign him now. Moreover, Real Madrid still has no a top striker, they only signed Joselu. I think Joselu isn't enough to compete for UCL title.
Indeed, after the departure of Benzema, they still do not have a replacement that is at least equal. And with Mbappe, this would be an extraordinary thing, but it's still wishful thinking at this time, because it's still just rumours. But indeed, the rumors in the current transfer market are stronger than before. If previously PSG could make such an attractive offer for Mbappe, this season might be different again. But, will Mbappe return to how he used to be, pressing his desire to go to Real Madrid and stay at PSG for certain reasons and offers.
Fiorentino Perez's decision to sign Kylian Mbappe isn't just because of the fact that he wants the perfect replacement for the position the Karim Benzema who just left at the club at the beginning of the summer transfer window but also because of his admiration for Mbappe since his days as a Monaco player.
The Real Madrid president initially had an agreement with the player before it was discovered by Paris Saint Germaine which made the club to put him up for sale and to sell him for the highest bidder.
It's Real Madrid decision to forget about Mbappe or outbid any other club that's interested in the services of the Frenchman this summer transfer window.