According to Goal, Carlo Ancelotti's side have submitted an improved bid of €170m for the 22-year-old after their opening offer was rejected. But the Ligue 1 giants have officially revealed that the Frenchman wants to leave the club after turning down a new contract.
The report goes on to state that the club are working behind the scenes to trim down the squad, with either Hazard, Marco Asensio, or Rodrygo set to be offloaded if they complete a deal for Mbappe.
Los Blacos have already made Gareth Bale, Luka Jovic, and Mariano Diaz available for transfer earlier in the summer, and are now pushing for multiple departures before the window closes on August 31.
Hazard has been linked with a return to Chelsea, but Goal claim he intends to stay put and fight for his place in Ancelotti's starting XI.
PSG sporting director, Leonardo, admitted this week that Mbappe wants to leave the club, but hit out at Madrid for what he called "illegal" conduct in contacting the forward.
"In terms of our position on Real, it seems like a strategy to try to get a no from us, to show that they have tried everything and to wait for a year to get him for free," Leonardo told RMC Sport.
"For the last two years, Real Madrid have been behaving like this, it is not correct. Illegal even because they contacted the player. It is unacceptable for us, because it is not correct. It is proof of the strategy: an offer comes 1 year before the end of his contract and 7 days before the end of the window. They want us to reject to show to Kylian that they tried everything and to start negotiating for next year.”