However, it seems as if the 2018 World Cup winner was due to sign for the Spanish giants, according to a surprising claim from former PSG midfielder Jerome Rothen.
"I know from club sources that a deal to take Kylian Mbappe to Real Madrid was almost done," Rothen told Radio Montecarlo.
"But with what has been happening, I'm sure that Mbappe's arrival at Real Madrid will be postponed."
"There is no way that Mbappe will extend his contract with PSG.
"They will have an agreement between them in place because PSG agreed to let him go this summer. In my opinion, it's just a question of time."
Los Blancos manager Zinedine Zidane has previously spoken about his admiration for Mbappe, something which did not sit well with PSG director Leonardo earlier this season.