The youngster has started only two Premier League matches this season, while he was hauled off at half-time in one of them.
The 23-year-old does not believe that he has the trust of manager Ange Postecoglou.
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Estadio Deportivo say Gil stayed at Spurs in January to try and prove himself.
However, he is close to accepting that he may not have a way back under Postecoglou.
Gil wants to leave permanently if he does exit, as he is tired of making loan moves.