According to Goal.com, Real Madrid offered even the amount that PSG wanted from them at the beginning (€220m). But PSG still turned down the offer. It looks like they have already run the risk of losing him for free. Because PSG really want to achieve the Champions League title in this season. They have a very capable team now. With Neymar, Messi and Mbappe, there is no opponent which they can't beat technically.
I assume that Real Madrid will offer a contract to Mbappe in January and Mbappe will join the team in the next summer.
If Mbappe should switch to Real Madrid, then there is a chance for Eden Hazard to go.
After Cristiano Ronaldo left Juventus Turin, there was not enough time to find a replacement. Juventus will look at signing Eden Hazard (contract at Real until 2024). He does not seem satisfied since his move from Chelsea to Madrid. There is probably the chance of a deal and Real can better pay the high salary of Mbappe.