The report quotes Turkish football agent Mesrun Izzet who claimed the Nigerian international is open to a Besiktas move as he wants first team football.
“Mikel did enquire about Besiktas and there were talks (but) it all depends on what their board decide to do,” Izzet said.
“Money is of course important but Mikel wants first-team football if he is to move.“
Mikel would almost be certain to lock down a first-team place at Besiktas and the Black Eagles would also be able to offer Champions League football.
The Istanbul giants won the Super Lig title last season and want an experienced central midfielder to strengthen the side ahead of their Champions League campaign.
Mikel has won the Champions League, Europa League, two Premier League titles, four FA Cups and two League Cups for the Blues.
It remains to be seen whether Antonio Conte has plans for Mikel in his side next season.
The powerful midfielder made 33 appearances in all competitions last season and has a year remaining on his current deal.