I am not sure that the transfer of Mbappe will happen in the next transfer window, because Paris Saint-Germain, unlike for example Barcelona, has no problems with either finances or financial fair play and therefore can afford to play a risky game and not sell Mbappe now, hoping to convince the player to stay in the team and extend the contract later.
The point isn't about the money or financial situation of both clubs, but Mbappe seems no longer interested to stay in PSG. If PSG cannot convince him to sign his contract extension, then probably PSG will get nothing if Mbappe decides to leave in the next transfer window. In this situation, I assume PSG is better to sell Mbappe in this transfer window to have some transfer fees. PSG also can start to plan for a replacement for Mbappe as soon as possible. This will be effective than spending time to force Mbappe to stay.
From some media I have seen PSG are really betting on this they keep trying to hold mbappe while Madrid also understands the situation that it will not get mbappe this season
Madrid hope to get him free next season actually it's not a bad idea, it's just that Madrid have had to go through this season with a player crisis