Sergio Ramos left the club on a free transfer over the summer, while Raphael Varane moved to Manchester United, with the 28-year-old Frenchman seeking a new challenge.
David Alaba joined Los Blancos on a free transfer, but Carlo Ancelotti’s side are short of experienced options in the middle of the park.
According to Calciomercato, Madrid are keen to strengthen at the back and have earmarked De Ligt as the ideal signing during next summer’s transfer window.
The 22-year-old Dutchman still has three years left to run on his contract at San Siro.
De Ligt has made 77 appearances for the Old Lady since arriving from Ajax.