Kavlak played under Bilic during the 46-year-old’s two-year spell at Besiktas.
“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.
“I was very lucky to work under a manager like him. He still follows our games closely.”
Bilic was appointed as West Ham manager after leaving Besiktas at the end of last season.
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.
Kavlak has been sidelined this season due to an injury and is yet to make an appearances for the Black Eagles.
Besiktas take on Trabzonspor in the Turkish Super Lig on Sunday. Their game against Mersin Idmanyurdu last weekend was abandoned due to poor weather conditions.