The 28-year-old is high up on the Black Eagles shortlist of potential signings this summer as Besiktas look to strengthen their central midfield.
Besiktas are targeting an experienced midfielder with a proven track record of top level football as they have booked a place in the Champions League next season after winning the Super Lig title.
The Nigerian international has won the Champions League, Europa League, two Premier League titles, four FA Cups and two League Cups for Chelsea.
Besiktas face uncertainty over the future of Atiba Hutchinson and already lack depth in central midfield.
The Blues reportedly want £7.7 million for Besiktas target John Obi Mikel according to the Express.
Mikel has just a year remaining on his contract and Antonio Conte has yet to make a decision on his future.