According to the Sun newspaper, the Nigeria international turned down a £110k-a-week offer from the Istanbul Giants back in January.
The 29-year-old instead opted to remain at Chelsea and is now in line to receive a contract extension.
Mikel has just one-year remaining on his current contract but Chelsea have yet to offer him a new deal.
Galatasaray are currently facing financial difficulties and have been suspended from European competitions for a season after failing to meet Financial Fair Play regulations.
Mikel has been closely linked with a move to Turkey in the past in fact Besiktas were on the verge of signing him last summer according to football agent Mesrun İzzet.
İzzet told Turkish sports radio station Radyospor that he had a mandate from Mikel’s agent to hold talks with Beşiktaş on behalf the Nigerian international.
“Mikel wanted to come to Turkey but Chelsea wanted a defensive midfielder as well. When they failed to sign Pogba Jose Mourinho decided to keep hold of his player,” İzzet told Radyospor.