The 27-year-old has been deemed surplus to requirements by Liverpool after an injury-plagued season with the Premier League champions.
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Chiesa only managed to make 14 appearances across all competitions for Arne Slot’s side, scoring two goals in the process.
According to Calciomercato, the winger has turned down the chance to join up with Mourinho in Turkey as he pushes for a move back to Italy.
Atalanta and champions Napoli have both been linked with moves for Chiesa, although neither are yet to make an offer.
Liverpool are keen to offload the Italy international as they seek to break the British transfer record for a second time this summer with a bid for Newcastle’s Alexander Isak.