Haber365 reports the 31-year-old Ukraine captain has already agreed a contract with the Turkish giants, where he will receive €4.5m-a-year.
Yarmolenko's deal with West Ham runs until 2022. It's suggested the Irons will not interfere with the player's departure.
Previously, the striker was interesting Galatasaray, which offered him a contract in January.
Last season, Yarmolenko played 15 matches in the English Premier League.