Real are understood to be interested in landing Mbappe, as well as his team-mate Neymar.
The Bernabeu club have already issued a statement refuting claims of a £275m bid for Neymar this week.
“Given the information published in the last hours referring to an alleged agreement between Real Madrid CF and PSG by player Kylian Mbappé, Real Madrid says they are flatly false,” the statement reads.
“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.”
Real are said to be pushing ahead with their summer transfer plans despite the World Cup currently taking focus away from domestic football.