The 28-year-old Nigerian international is into his tenth season at Stamford Bridge but has seen his first-team chances restricted in recent campaigns.
Mikel is now little more than a bit-part player in Jose Mourinho’s set-up, making just one Premier League start this term, and could well be ready for a fresh challenge.
The likes of Nemanja Matic, Ramires and youngster Ruben Loftus-Cheek are now ahead of Mikel in Mourinho’s pecking order.
Besiktas failed with a summer move for Mikel but may feel more confident of sealing the deal when the transfer window re-opens.
Mikel has made 339 appearances for Chelsea, helping the club to two Premier League titles as well as Champions and Europa League crowns.