Kavlak has missed the entire season with injury but was the backbone of the Besiktas for the previous two seasons under the stewardship of West Ham boss Slaven Bilic.
Bilic is a self-confessed fan of the central midfielder and helped develop Kavlak into one of the most sought after midfielders in the league during his time in charge of the club.
Kavlak is close to making a full recovery from his shoulder injury and is reported to be keen on playing under the stewardship of Bilic once again.
The hard working midfielder recently stated that Bilic was like a father figure to him during his time in charge of the Istanbul giants.
“He [Bilic] was like a father for me. He always supported me and gave me freedom to express myself,” Kavlak was quoted as saying by the daily newspaper Radikal.
The 25-year-old joined Beşiktaş for £600,000 from Rapid Vienna in 2011 and has eight goals and 14 assists in 144 appearances for the Black Eagles.