Gittens, 22, only joined Chelsea from Borussia Dortmund last summer, but injury issues meant he struggled during his first season at the club.
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The winger started just five of his 16 Premier League games, with his only goal coming in the League Cup.
According to TalkSport, Serie A side Roma are keen on Gittens as they continue their search for a new left winger this summer.
Chelsea have turned down a loan offer from them, however, and Gittens is expected to be part of Xabi Alonso’s side this season.