Real Madrid don't need to pay that much money right now, they'd better wait a bit and propose to Mbappe in January 2024 when Mbappe becomes a free agent. For PSG, this is not the best option as they could be left without money and without Mbappe, but they will have time to convince him to extend his contract and thus keep this talented player. Real Madrid are already stepping up their attack and of course they would like to have Mbappe in their team, but apparently this is not a priority right now.
If we wait until 2024, I think it will be a bit long because what Real Madrid wants is that at the start of the season, Mbappe is already at Real Madrid to be able to dominate the game this summer. but if indeed Mbappe is retained by PSG for me it will only be in vain because Mbappe's desire to win the UCL title has long been and maybe only by joining Madrid can he achieve what he wants.
I think it will be as late as August if you ask me, because first of August means that if Mbappe hasn't extended his contract by that time, it is automatically not extended after that as well, which makes all of this rumor become real. In that case PSG will openly put him on the market, maybe even go as far as putting a value tag on him as well, if that were to happen I am sure that teams will line up to pay for it, and yes he will be very expensive and not many teams could afford it, but not like the ones who can will stop, they will offer him.
First place on that run is Real Madrid, not only because they are rich but also Mbappe would love to play for them, he has said this himself multiple times, it is his dream team since he was a kid.