It is all up to PSG and whether they want to make some money selling Mbappe or not. I am sure they don't really need the money, so it is possible that we will see Mbappe play for PSG for another year against his real desire and intention.
I wonder whether you just compared the 24 years old Mbappe to the 35 years old Messi or whether you compared the 24 years old Mbappe to the 24 years old Messi? Mbappe has a long way to go to score the numbers that Messi scored at age 24. At age 24 Messi had 68 scorer points in La Liga only, with 50 goals scored and 18 assists. He also scored 14 goals in the Champions League.
Just as a comparison, Mbappe had 34 scorer points in Ligue 1 this season. That is 50% of Messi.
Mbappe can still become the best of the best but he won't become that playing for PSG.
I think it's not about "needing" money, I think it is being screwed financially when you don't have to, basically just like getting scammed at that point, just because you are rich doesn't mean that you would want to be scammed. Mbappe could be sold for 100+ million, do you think a single season of Mbappe worths more than 100+ million?
I do not think so, I think he worths as much as 50-60 million at most for a single season, probably not even as much but inflation made these salaries go up, however not twice that much and they could make twice that amount. Then they could use that money to buy another player, which would be fine for them. So they need to convince him to leave, I am sure Madrid would be willing to pay, just sit Mbappe down and explain him that he will play his childhood dream team.