The Chelsea goalkeeper has previously stated his desire to return to Spain after enjoying a successful spell with Atletico Madrid before becoming Chelsea's first choice goalkeeper.
Real Madrid have been linked with the Belgian already and Courtois could be involved in a high-profile swap deal with Madrid midfielder James Rodriguez.
Rodriguez previously stated that he would consider his future with the club after falling out of favour in the past couple of seasons.
Chelsea are rumoured to be interested in the Colombian and therefore could use Courtois in order to try to persuade Madrid to let go of the player.
However, a deal in January is impossibe as Madrid are banned from signing players until the summer, but an agreement could be made at the end of the season.