If PSG decided to stop Mbappe this season then that is very big risk because if he decides to leave next season that will be on a free transfer which would cost the club a big fortune thus losing millions of Euros, the only way forward is Mbappe to give assurance to the club that he is staying with the club for a long term basis and ready to sign a new contract, however with some recent speculations of his purported move to Real Madrid is unsettling his club, of course Real Madrid needed a striker to replace Benzema who had left the club while the club is already on the move to bid for and sign Harry Kane, however I think Real Madrid will give up on signing him for Mbappe.
They already said that if he doesn't sign until 1st of august (automatic no renewal) then he is open for sale, and he is open for sale even right now because he hasn't signed it yet, the only way he would ever be off the table could be him getting that extension otherwise he is just on the market.
Not a ton of teams can afford him though, that's the issue, and not like he would go to any team neither, so there are very few teams that can both afford him and convince him at the same time. lets see what's going to happen, maybe one or two premier league teams, Madrid, and as I heard Bayern is getting ready to make an offer as well, its not official yet but seems like they probably won't be able to afford him. It will be a very very exciting summer without a doubt.