It's unlikely to happen. PSG has been threatening him to be unplayed for this season. PSG will be putting him on the bench this season. That's why PSG is looking for a new striker. PSG still hopes mbappe leaves from the club.
Just because PSG is looking for a new striker and it doesn't mean mbappe will be moving to the real madrid. There's no talk between PSG and madrid. I think that mbappe must accept it if he gonna be benched by the club instead of given chances to play next season. PSG is not having a lot of choice. Mbappe is still trying to stay even longer in the club no matter what kind of sanction will be given by PSG. Madrid can't afford very big amounts of money to buy him before the club sells some players first.
Well, I don't know. If you look at this situation from the outside, Mbappe has already made a lot of efforts to leave Paris Saint Germain, consistently spoiling relations with the club's management, although it is clearly financially beneficial for the player himself to stay at the club for another season. Therefore, if Mbappe has a chance to leave for Real Madrid in a good way already in this transfer window, then I think that the player will take advantage of this opportunity with pleasure. I personally have no other explanation for Mbappe's latest demarches.