The report claims Mourinho's appointment will be confirmed sooner rather than later, and the Portuguese manager wants to bring the Germany international midfielder to Stamford Bridge with him.
The 26-year-old Khedira moved to the Bernabeu after starring at the 2010 World Cup alongside Mesut Ozil, and Mourinho has identified Khedira as the man to anchor Chelsea's midfield.
Khedira would likely be signed as a direct replacement for John Obi Mikel, while Mourinho is not thought to be a fan of playing David Luiz in the defensive midfield role.
The former-Stuttgart star was one of Mourinho's first signings when he took over as Real Madrid boss, and he only has two years remaining on his contract in the Spanish capital.
Still, the report claims Chelsea could expect to pay at least £20m for the midfielder.
One player who will be swapping the Bernabeu for Stamford Bridge this summer will be Michael Essien. The Ghanian's loan spell at Real Madrid comes to an end in the next few weeks, and he'll be part of Chelsea's first-team plans next season, according to the report.
But the future of Kevin De Bruyne remains uncertain, with two Bundesliga clubs thought to be keen on his signature.
But the 20-year-old is highly-rated at Chelsea, despite not having played a Premier League game, and the club are reportedly reluctant to let him go permanently.
Another loan move next season could be on the cards, though.