West Ham linked with Slaven Bilic
The 46-year-old Bilic, is reportedly now favourite to replace Sam Allardyce at Upton Park, and has been in charge of the Turkish side since 2013.
"I won't be Besiktas's manager next season," said Bilic. "I'm proud of what I've done here."
West Ham confirmed on Sunday that Allardyce would not be manager next season.
Ex-Croatia international Bilic spent just over a year at the Hammers from 1996, making 48 appearances for the club.
Since retiring as a player, he spent six years in charge of the Croatia national side before a spell at Dynamo Moscow.
He failed to guide Besiktas to the Turkish league title in his two years at the club and Sunday's 2-0 defeat to Galatasaray meant they missed out on Champions League qualification for next season.
"As I said before, I am the first one who is going to take responsibility for not winning the league for two years," he added. "I have already made my decision."
Allardyce meanwhile has said he plans to take some time away from the game.