Los Blancos failed to convince Paris Saint-Germain to sell Mbappe over the summer but are expected to return for the Frenchman either in January or at the end of the season, when he could be available on a free.
According to todofichajes, Carlo Ancelotti's side are prepared to sell Hazard in order to make room for the World Cup winner to arrive at the club.
The report claims that the capital giants will listen to any offers that might be presented for the former Chelsea attacker during the January transfer window.
Hazard, who still has three years left to run on his contract at the Bernabeu, has scored just five times in 47 appearances for Real Madrid since a big-money move from Chelsea in July 2019.
The 30-year-old was handed a start against Celta Vigo in La Liga on Sunday night but was withdrawn in the 66th minute, and the Belgian's replacement Eduardo Camavinga went on to net a debut goal.