The Nigerian midfielder has not yet decided whether he will join the Russian club and says he has grown frustrated at his lack of playing time at Stamford Bridge
Italian sources had claimed on Thursday that the cash-rich club were lining up a bid for the Nigeria international as they hope to make some last-minute purchases before the Russian transfer window shuts down on Friday.
Obi Mikel has been at Chelsea since 2006, when he arrived at Stamford Bridge from Norwegian club FK Lyn.
He has been a bit-part player at the Blues this season, making 12 starting appearances since Andre Villas-Boas took over at the club in the summer.
"It is true that I have been in contact with some Anzhi officials, who wanted to know if there was the possibility that I moved to Russia, but I have not yet given them an answer," Obi Mikel told MTN Football.
"I am a player of Chelsea and changing clubs is not something to be made lightly. I love Chelsea and I am taking the time I need to make a decision.
"My main goal is to play on a regular basis and that has not happened lately. I hope that after my latest injury, I will be able to play regularly again."
Mikel has made 37 appearances for Nigeria, scoring twice in the process.