Los Blancos could seek a long-term solution at centre-back next summer.
Real Madrid are among the teams monitoring Chelsea centre-back Antonio Rudiger, according to Sky Sports.
The defender will be out of contract after this season, and if an extension is not agreed upon by January, he is allowed to begin negotiations for a pre-contract with other clubs.
Given the losses of Sergio Ramos and Raphael Varane, Real Madrid could be tempted to make a move for the German international ahead of next summer.
Sky Sports
