The Germany international was heavily linked with a big-money move to the north London club last summer, but the midfielder stayed put at The Bernabeu.
However, Khedira has struggled with injury problems throughout the season, whilst the 27-year-old has falling down the pecking order at Los Blancos.
Schalke chief Tonnies is confident that the World Cup winner would prefer a move back to Germany, appearing to claim that S04 are leading the race to land Khedira.
“It’s my impression that Khedira wants to return to the Bundesliga,” Tonnies told BILD Sport.
“I believe he does not doubt that for a second. I believe there aren’t too many clubs in Germany coming into question.”
Khedira’s Germany team-mate Mesut Ozil moved to the north London outfit in a club-record £42.5m deal from Madrid in 2013.
The World Cup winner has made just 17 appearances in all competitions for Los Blancos this season after falling out-of-favour under Real Madrid manager Carlo Anecelotti.
Khedira has won La Liga, the Champions League and the Copa del Rey since moving to the Spanish capital from Stuttgart in 2010.
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