Spanish newspaper AS claims that Mourinho will look to bring the Germany international - who was a summer transfer target for Manchester United - to Stamford Bridge "at any price".
Reports earlier this week suggested Khedira was open to holding talks with Chelsea over a potential January move to the club.
Real Madrid signed Asier Illarramendi from Real Sociedad in a €39m deal over the summer, and while the Spain under-21 star is viewed as a long-term replacement for Xabi Alonso, he still crowds the Bernabeu midfield.
Luka Modric has also emerged this season under Carlo Ancelotti, putting further pressure on Khedira's place.
The German star is still first-choice under the new Madrid boss, but he's thought to be keen to link up with Mourinho again.
And he was linked with a move to Old Trafford in the final days of the summer window, with United boss David Moyes reportedly lodging a £35m bid for his services. But a move to United failed to materialise.
He played some of his best football under Mourinho, and is believed to be keen to test himself in the Premier League after three years in Spain.
A £35m price-tag for Khedira has been mooted this season, although the report claims Chelsea would be willing to go beyond that to sign the midfielder.
Following injury to Marco Van Ginkel, Mourinho has found himself short of options in the middle of midfield.
John Obi Mikel, Frank Lampard and Ramires are the club's only senior central midfielders - although David Luiz could potentially step into the role if required.
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