The France international was strongly linked with Los Blancos during the summer transfer window, but Carlo Ancelotti's side were unable to convince the French giants to sell.
Mbappe's contract in Paris is due to expire next June, though, meaning that Real Madrid, as it stands, would be free to hold talks with the World Cup winner over a pre-contract at the start of 2022.
However, according to AS, Mbappe has already made his decision, with the 22-year-old expecting to move to the Spanish capital at the end of the 2021-22 campaign.
The report claims that money has played no role in the Frenchman's decision, and PSG would not be able to convince him to stay even by making him the best-paid footballer in world football.
Mbappe has scored five times and registered six assists in 12 appearances for Pochettino's side during the current season.