The legendary Turkish boss left the club earlier this week following a bust-up with president Unal Aysal after delivering two Super Lig titles in as many seasons.
Mancini, meanwhile, has been out of work after being sacked by Manchester City back in May following the English side's loss to Wigan in the FA Cup final.
Galatasaray legend Hakan Sukur has confirmed that the two parties are close to reaching a deal but have a difference in opinion concerning the rest of the backroom staff.
"I have a mutual friend with Mancini and I spoke him and Galatasaray and Mancini are in the final stages," he is quoted as saying by Sporx.
"There is a difference only about the assistants. Whether or not Umit [Davala] and Hasan San will remain. Mancini wants to bring his own assistants. I expect this issue to be resolved."
Galatasaray fans showed up the 1-1 draw with Caykur Rizespor on Saturday wearing Terim masks in a show of support for the 60-year-old.
Source: Manchester City MAD