As far as I can see the best thing PSG can do about their players like Mbappe who won't extend his contract is to keep him for another season when his contract ends and until that time they can use this player to achieve their goals. Also, PSG would use another coach and Luis Enrique can be a good option for them in the next season while they still can have Zidane as their first priority.
But the thing is Mbappe has stated that he will not renew his contract after next year and that has PSG starting to panic now. We cannot control the will of players who don't want to agree with the club's wishes and players like Mbappe should start being freed from the responsibility of the Paris capital team.
Moreover, he has never won a champion's league title, of course he will come to a club that has that goal and will not stay at PSG. We know Mbappe's goal is to one day become the best player in the world and if he was still with PSG that goal would never be achieved.