The Brazilian has made just nine appearances for Real since moving to the club three years ago and has not featured for Zinedine Zidane's side this season.
Silva was set to join Portuguese side Sporting Lisbon last year on a season-long loan but the move fell through when an irregular heartbeat was detected in his medical.
The 23-year-old defensive midfielder, who began his career at Cruzeiro, is under contract with Real until June 2020.
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(Reporting by Adriana Garcia; Editing by Toby Davis)
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