PSG need to get money from Mbappe so they will not release the player. They will not terminate the contract and let Mbappe goes away as a free agent. They can reduce price at the end to sell Mbappe but they can hold the negotiation to bargain as highest transfer price as possible.
When the option to let Mbappe go on a free transfer, what happens is not profitable and PSG will definitely look for other options to prevent this from happening. There is a possibility that PSG will offer a new contract for one season and then Mbappe may leave at a price that is not too expensive, this option is made so that PSG does not suffer big losses.
Problem with Neymar is he is very vulnerable to injury and PSG can no rely on Neymar as latest seasons show that Neymar usually was in hospital by injuries when PSG need him most.
Neymar has always had problems with injuries and this condition has also harmed PSG because when they need him he can't play. Compared to Mbappe, Nyamar is more likely to leave PSG because his contribution last season was clearly not productive due to frequent injuries.
Yeah he has to sale off many players he does not plan to use in a new future to save salary budget for the club and to have vacant positions for new players. Definitely he does not want to lose Mbappe but the future of Mbappe is not controlled by Luis Enrique.
PSG doesn't need to think about saving the budget because the club owner has a lot of money for this problem. Enrique needs Mbappe in the next season because this player has the best quality at the moment and although Mbappe's future is not controlled by Enrique, his arrival to PSG holds great hope for them at this time.