The Mali international’s contract with Wolves expires at the end of the month meaning Besiktas will be able to sign him on a free transfer.
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.
The 27-year-old is keen on a move away from Molineux and is expected to leave at the end of the month.
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.
The Black Eagles are currently without a manager following the resignation of Slaven Bilic but Şenol Güneş has been closely linked with the Istanbul giants.