The report states that Bursaspor have made an offer for the 27-year-old who is currently out-of-contract.
Sako recently revealed his desire to play in the Premier League despite receiving offers form abroad.
“I have some offers from the Premier League and some from abroad, but I want to play in the Premier League,” Sako told the Express.
“I have offers from abroad but I’m not looking at them at the moment – I want to play in England.”
Sako joined Wolves from St Etienne for €3.8 million back in 2012. The 27-year-old has provided ten assists and 15 goals in 43 appearances for Wolves this season.
Beşiktaş finished the Turkish Super Lig season in third place and will play in the Europa League next season.