The report claims Chelsea have already opened talks with Real Madrid over a move for the Germany international, who had been heavily linked with Manchester United before his injury.
He's currently sidelined with a knee ligament injury, but Chelsea reportedly lead a list of suitors in the race to sign him before the World Cup.
Initial discussions between Chelsea and Real Madrid have taken place although nothing firm has been agreed.
United boss David Moyes attempted to sign Khedira in the summer transfer window, but ultimately settled for Marouane Fellaini after failed pursuits of Ander Herrera, Cesc Fabregas and Khedira.
Moyes may have now moved on from Khedira, with the latest reports suggesting his Germany international teammate Toni Kroos is United's top target.
Khedira is unlikely to feature at the World Cup in Brazil as he continues his recuperations from an ACL tear.
But Chelsea remain keen to bring him to Stamford Bridge for the start of next season.
It remains to be seen whether Real Madrid are open to selling the central midfielder - although the €38m capture of Asier Illarramendi last summer may hint at Carlo Ancelotti's long-term thinking.
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