‘The Special One’ coached the German international during his spell at the Bernabeu, where he was a key member of Los Blancos’ first-team.
Khedira is currently out of action with a knee injury, but that has not deterred the Blues from making him one of their top targets for the coming transfer window.
It is understood that discussions between the clubs have taken place, and that the Londoners are keen to make him a part of their squad later this year.
Real are undecided as to whether or not they will sell, but they may be open to a deal due to the emergence of Asier Illarramendi – who signed for them last summer.
Khedira himself may be open to re-joining Mourinho, after enjoying a successful period working under him.
Manchester United have also been linked with the ex-Stuttgart ace, and may revive their interest in six months’ time after seeing a late move his signature last year fail.
Khedira’s World Cup berth is currently in doubt due to his fitness concerns, but he is expected to make the Germany squad if he can recover in time.