Although the French international player has less than a year left on his contract, Real Madrid are suspected of being willing to pay a £ 155m regional fee to sign him.
As it stands, PSG will still be officially debated whether they are ready to accept the offer, which seems to cause concern for the player and his long-term fans.
According to RMC Sport, Real Madrid officials are satisfied with the release of any negotiations before the end of the summer transfer market window.
Kylian Mbappe is said to be unwilling to extend his stay at Parc des Princes, a condition that will allow him to sign a pre-contract contract early next year.
PSG are likely to continue their efforts to try to agree to new terms with the 22-year-old.