Former Everton boss Marco Silva also reportedly sees Gray as a transfer target for his Fulham side this summer, though now could face competition from Turkish Super Lig giants Besiktas.
That is according to Turkish news outlet Sabah, who report that Everton could want a fee of around £10m for Gray, which would earn the Blues a substantial profit.
Demarai Gray sale could boost Everton transfer funds
A regular starter under Frank Lampard, Gray was used increasingly sparingly following Sean Dyche’s January appointment and it seems that the Everton boss doesn’t fancy the 27-year-old.
Indeed, after starting every Premier League game under Lampard last season, Gray was dropped to the bench for Dyche’s first game in the Goodison Park dugout as the Blues beat Arsenal 1-0 in February.
Gray would subsequently start four more Premier League games on the substitutes bench, including home fixtures to Leeds and Newcastle United, and away visits to Leicester City and Brighton & Hove Albion.
In 33 Premier League outings overall last season, Gray managed four goals, including a memorable strike away at Manchester City, with one assist provided.
The Jamaica international was often deployed as a makeshift centre-forward in the absence of Dominic Calvert-Lewin, though is at his most dangerous cutting inside from the wing.
However, as Dyche looks to rebuild Everton’s threadbare forward line, cashing in on the inconsistent Gray wouldn’t be the worst thing, provided the fee is reinvested wisely.