Mikel and Drogba were teammates at Chelsea until the Ivorian international left Stamford Bridge in the summer of 2012.
And Mikel admitted he asked his old colleague for advice about moving to Galatasaray after it emerged that the club were interested in signing him.
"I'm very pleased with Galatasaray's offer," Mikel told Sabah, a Turkish newspaper.
"I asked Drogba for advice and he told me that Istanbul is a fantastic city, that Galatasaray is a huge club and that I have to make the move.
"I have played at Chelsea for a long time and it's now time for me to leave.
"I'm still only 26 and it's great to receive an offer from a club [Galatasaray] playing Champions League football and doing well in the competition."
Mikel was signed by Mourinho in 2006 after a long drawn out transfer saga involving Manchester United, but the 'Special One's' return doesn't look like preventing his exit.
Mikel continued: "Talks have reached an advanced level between Chelsea and Galatasaray. Chelsea won't make the move difficult and regarding my salary there won't be a problem.
"All that is left is for the clubs to reach an agreement."
Mikel has been an important part of the Chelsea first-team squad in recent seasons, but talk of a reshuffle under new boss Mourinho could pave the way for him to leave the club.
Mourinho has been linked with several big-money moves, and the Chelsea boss would be expected to at least recoup some money before spending Roman Abramovich's cash.
That could explain Mikel's potential departure, with Chelsea capable of replacing the Nigerian international with David Luiz in a deep lying midfield role or Frank Lampard or even the returning Oriol Romeu.