The 25-year-old barely featured under new coach Jose Mourinho last season, making just four La Liga appearances, and with the arrival of midfield recruits Nuri Sahin, Hamit Altintop and Fabio Coentrao finds himself surplus to requirements.
Real signed Gago from Boca Juniors for just over 20 million euros in January 2007.
Earlier on Wednesday, Real loaned winger Pedro Leon back to Getafe, the club they bought him from in 2010.
Getafe have an option to make the move permanent at the end of the season.
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