The Paris Saint-German star only joined the French club last summer when he moved from Monaco for £140million.
But an impressive first season – and a stunning showing against Argentina at the World Cup – has attracted interest from some of Europe’s biggest clubs.
Real Madrid were interested in signing the 19-year-old 12 months ago but have refuted rumours they have re-entered the race.
A statement read: “Given the information published in the last hours referring to an alleged agreement between Real Madrid CF and PSG by player Kylian Mbappe, Real Madrid says they are flatly false.
“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.”