The France World Cup winner is a 2020 transfer priority for Florentino.
And Okdiario's Eduardo Inda, speaking on El Chiringuito, says the president knows it will take world record money to convince PSG to sell.
He revealed: "Real Madrid wants to advance the signing of Mbappé next summer.
"They have made calculations and the amount would not fall below €300m."
However, it's also claimed if Mbappe signs a new contract tabled by PSG, then Real will abandon the move.
A Madrid source told Okdiario, "If Mbappé renews, he will be tied the PSG for life and it will be impossible to get him out of there."