The Germany international was heavily linked with a switch to the north London club last summer, however a move failed to materialise as Arsene Wenger failed to significantly strengthen his midfield.
However, Khedira continues to be linked with a move to the Premier League amid reported interest from Premier League leaders Chelsea and under-fire Manchester United manager Louis van Gaal.
Quizzed about a potential move to Schalke after a 4-3 defeat by the German side in the Champions League on Tuesday night, Khedira is quoted as saying by talkSPORT: “Am I Open to Schalke? I am open to many teams.”
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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