The 27-year old winger is the subject of interest from several clubs this summer and Premier League outfits Crystal Palace and Fulham are keen on him.
Last season, Gray featured in 33 league games for Everton and helped the Toffees keep their Premier League status.
In the ongoing transfer window, Everton are going through financial constraints and the club might be willing to sell Gray to ease their situation.
Now, according to Turkish daily Sabah, Besiktas have joined the hunt for Gray and they have made an enquiry for the Everton winger.
It is said that the Toffees have slapped a £10m price tag on the Jamaican international, who has one more year left on his contract with the Goodison Park outfit.
Fulham are ready to offer £7m to sign the winger and Crystal Palace have yet to submit any official bid.
The Eagles are in the market for Wilfried Zaha’s replacement and have been linked with Gray.
Now it remains to be seen whether any club will be ready to meet Everton’s demands to take Gray away this summer.
