Manchester United target Paul Pogba is also on the radar of Real Madrid, according to Italian reports.
The Juventus midfielder, who has been instrumental in his team's success this season, has caught the attention of many of Europe's top clubs. Despite being a pivotal player for La Vecchia Signora, Pogba is not interested in renewing his deal with the Italian giants.
Los Blancos are having excellent results this season but strengthening the midfield is one of their main goals ahead of the summer transfer window. Xabi Alonso, Luka Modric, Asier Illarramendi and Sami Khedira have a fixed place in Madrid's next project, but not Angel Di Maria.
According to La Gazzetta dello Sport, Ancelotti wants to strengthen the midfield with the arrival of a pivot with Pogba's attributes, and he is confident they can land him from Juve in the summer.
Real Madrid have been interested in bringing him to the Santiago Bernabeu ever since his excellent performance at the Euro Under-17 championships in 2010.
The powerful Frenchman has thrived in Turin since his move from Manchester United, which was precipitated by a falling out with Sir Alex Ferguson in 2012. Now the Red Devils want to re-sign him but face a mountain of problems, including his price tag and the club's current situation in the Premier League.
But Real's main problem is Paris Saint-Germain's interest. The French club have been heavily linked with a move for the 20-year-old and their president, Nasser Al Khelaifi, is keen on bringing the youngster to the French capital and would be willing to pay €70m for him.