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.
If we look at Mbappe's rumored journey with Real Madrid, it has been going on for two years and until now the results are still the same without any significant clarity. Maybe for Mbappe if he leaves now he can do it, but he doesn't want to lose the bonuses he gets when his contract expires next year and many sources have said this. On the other hand, PSG don't want to lose if Mbappe is a free agent and therefore PSG's owners insist on putting pressure on Mbappe whether he will extend the contract or leave now. I think the particular offer you are referring to, I understand very well what you are thinking and this could happen if Mbappe was still thinking about money over his career.