It is the second time in as many days that Los Blancos have put out such a statement after it had been claimed on Spanish television on Tuesday night that they had submitted a €310m bid for Neymar and were ready to offer the player a seven-year contract worth €315m.
Real labelled the Neymar story 'false information' and the statement on Mbappe was similar.
"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."
Mbappe, who is nominated for the 2018 Golden Boy award and could become the first ever player to win the coveted prize twice, has lit up the World Cup in Russia this summer.
The 19-year-old netted the winning goal for France against Peru in the group stage to seal his country's safe passage to the knockout rounds, before destroying Argentina in the last 16 and ending Lionel Messi's hopes of concluding his international career with a World Cup trophy.
Real are yet to make any summer signings since winning a third successive Champions League title at the end of last season, while fringe players Philipp Lienhart and Omar Mascarell, both of whom spent 2017/18 out on loan, are the only departures.