That's according to Spanish newspaper El Confidencial, who report that Real Madrid have all but given up on convincing the Germany international to sign a new contract extension.
The 27-year-old midfielder has just 11 months left to run on his current deal, and has attracted interest from both Arsenal and Chelsea.
Arsenal in front?
Arsenal were believed to be leading the race to sign him, and reports in the last month have claimed the Gunners are ready to sanction a £20m bid for the World Cup finalist.
But a sticking point remains his wages - Khedira reportedly wants £150,000-a-week to leave the Bernabeu, slightly too steep for Arsenal's budget. That wouldn't be a problem for Chelsea though, who already have a number of players on wages significantly higher than that figure.
Mourinho a fan
Stamford Bridge boss Jose Mourinho remains a big fan of Khedira, having signed the midfielder when he was Real Madrid boss. He's been linked with a number of central midfielders, despite the acquisition of Cesc Fabregas from Barcelona.
Juventus star Paul Pogba would be the headline-grabbing name, but Khedira would be a cheaper option without sacrificing quality.
Alternatives for the Gunners
Arsenal meanwhile are believed to be shopping vice-captain Mikel Arteta, with clubs in Italy interested. If he does depart, Arsene Wenger would need to strengthen in the middle of midfield.
Lars Bender from Bayer Leverkusen and Morgan Schneiderlin of Southampton are two potential alternatives.