Following weeks of speculation, it was claimed in France overnight that a £239m agreement had been reached between Madrid and PSG for Mbappe's signature.
A statement on the European champions' official website has poured cold water on these claims, however, with no offers being tabled for the 19-year-old.
"Given the information published in the last few hours referring to an alleged agreement between Real Madrid and PSG for player Kylian Mbappe, Real Madrid says they are flatly false," the statement read.
"Real Madrid has not made any offers to PSG or the player and regrets the dissemination of this type of information that is not contrasted with the parties."
Manchester United have also been credited with showing an interest in Mbappe, who cost PSG £166m to acquire from rivals Monaco.