The Blues are reported to be considering offering Mikel as part of an exchange deal to secure the signing of Morgan Schneiderlin.
Arsenal are also rumoured to be in the race to sign Schneirderlin.
Mikel joined Chelsea in 2006, has made 329 appearances for the Blues winning the league, FA Cup and Champions League titles.
Galatasaray have also been closely linked with the Nigerian international.
The Lions will have more flexibility in the transfer market next season due to changes in the foreign player ruling.
The Istanbul giants will be able to sign 14 and play 11 foreign players at any one time following the rule changes implemented by the Turkish Football Federation (TFF) that come into effect next season.
The Lions are currently third in the league but trail league leaders Fenerbahçe by just a single point.
Galatasaray have competed in the Champions League for the last three consecutive seasons.