According to reports, the Spanish outfit have already made initial contact with the Italian, and it will be interesting to see if he agrees to take over from Zinedine Zidane next season.
The Frenchman resigned from his position earlier this month, and Florentino Perez is looking for a quality replacement.
The likes of Max Allegri, Antonio Conte, Mauricio Pochettino, Raul Gonzalez and Xabi Alonso have all been linked as potential replacements, but Carlo Ancelotti represents a much safer appointment.
The Italian is an experienced manager who has won trophies consistently throughout his career. Furthermore, he knows the Spanish club well from his previous spell as the manager at Santiago Bernabeu. It was Ancelotti, whom Zinedine Zidane had assisted before the Frenchman was reinstated as manager of Los Blancos.
Ancelotti helped them win the coveted La Decima, and he also won the Copa del Rey, Supercopa de Espana and a Club World Cup title during his time at the Spanish club.
It will be interesting to see if Real Madrid can lure him away from the Premier League club this summer.
Everton have backed Ancelotti in the market since his arrival, and they are looking to build an ambitious project with him at the helm. His departure now would be a damaging blow for the Toffees.
It will be interesting to see if Ancelotti is willing to abandon his project at Goodison Park in favour of a return to his former club.