According to the Express, Leicester City have offered the Mali international a lucrative contract.
The report goes onto state that The Mali international has decided to leave Wolves in the summer when his contract expires.
Besiktas have been linked with a move for Sako by the Milliyet. The Black Eagles will be able to sign him on a free transfer.
However, 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.
Wolves ended the Championship in seventh place with 78 points in 46 games.
Beşiktaş finished the Turkish Super Lig season in third place and will play in the Europa League next season.