Mbappe joined PSG last year on an initial loan deal that will become permanent this summer in a deal that will see him become the second most expensive player in history.
However, Madrid have been closely linked with the 19-year-old attacker, and it has been claimed in France that he is on his way to the Spanish capital this summer to replace Cristiano Ronaldo, who is reportedly set to joinJuventus after his shock revelation that he wants to leave .
The Spanish club insist that no such deal is in place, though, saying the reports are simply false.
"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," a 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."
Madrid have been closely monitoring Mbappe since his days at Monaco and the principality club's vice-president has said they made an offer worth €180m only to be knocked back as he opted to return to boyhood club PSG.
Mbappe scored 21 times in 44 games for the French club in his first season and has played a key role for the national team at the World Cup, having netted three times in four games.
The statement comes just over a day after the Champions League holders made an announcement to clarify that talk of another world record deal with PSG had been struck, after it was reported that they were set to sign Neymar this summer for €310m (£275m/$360m) .
Like Mbappe, the Brazilian has been continually linked to the Santiago Bernabeu outfit since arriving at the Parc des Princes team.