PSG have offered a salary increase and a long contract for Mbappe, but he is not tempted by a luxurious offer from PSG because Mbappe desire to play with Real Madrid is very strong. after not reaching an agreement with Mbappe, PSG must make a decision soon, because his contract will soon expire in June 2022. It would be a huge loss for PSG if they lost Mbappe on a free transfer. So PSG decision to let Mbappe go to Real Madrid was right.
Mbappe can be part of a new era that Madrid is trying to build, especially since Hazard has not been able to make a good contribution to Real Madrid. But Mbappe can't be on Real Madrid's list to play in the Champions League this season, because Mbappe has previously played with PSG.
Obviously it would be a big loss for PSG if Mbappe became a free transfer player and if it did succeed to Real Madrid it would definitely be better for the Real Madrid club later because on the one hand Mbappe is a very good player and also has qualified skills in playing, but if for this season, it is clear that he must stay with PSG, now when his contract expires with PSG, that's where we have to see where he will land.
PSG could have made a lot of money by selling Mbappe. But PSG does not seem interested in making money. They want to win the Champions League title. They will try their best to keep Mbappe in the team. My guess is that PSG management is still optimistic about Mbappe that maybe PSG will renew their contract with them and decide to stay at PSG.