The Brazil fullback has shone on-loan from Manchester City.
Girona would like to keep Couto for a third season, but risk losing him as interest grows from bigger clubs.
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talkSPORT says German champions Bayer Leverkusen and Italian giants Juventus are chasing the 21 year-old.
In addition, there is interest from several clubs in the Premier League.
City could be under pressure to sell Couto this summer as his contract expires in 2025.