Drogba scored 157 goals in 341 appearances over eight years for the Blues, including the decisive penalty in the 2012 European Cup win, and is expected to be heralded by home supporters during the Champions League last-16 second leg.
Former Manchester City boss Mancini suggested after the 1-1 first leg that Mourinho had invited him out to dinner and followed up on the eve of the match by promising to take up the offer, on one condition.
Mancini said: "If we win, sure. And I'll pay."
Asked two hours later if he would accept, Mourinho said: "No, because I have no interest.
"In my plans after the game, I don't have a meal with somebody that has the same job as I have and this is the only thing we have in common. The fact we both are football managers. Nothing else."
Mourinho and Drogba have more in common after working together during the most successful period in Chelsea's history.
The Portuguese returned to London with Inter Milan in 2010 en route to winning the European Cup and received an ovation from the home faithful before ending Chelsea's tournament.
Drogba admitted he would feel mixed emotions when he was asked if he would celebrate the winning goal at Stamford Bridge, if he scores it, but his loyalty is firmly with Galatasaray - for now.
"I might not celebrate, but if we win I'll be happy," Drogba said.
Drogba was asked if he could see a future at Chelsea, and said: "Of course, but just not now. I still want to play."
Reports surfaced earlier this year that Mourinho had offered the Ivorian a coaching role and the Chelsea boss anticipates Drogba will one day return.
"I don't think it's the right moment to speak about it," Mourinho said.
"He's a Galatasaray player. We know he's a free agent. We know he finishes his contract at the end of the season, but we know it's not the right moment (to discuss it).
"I think it has to happen one day. When, I don't know. As a player, as a coach, as an ambassador, next year, in four, five years, in 10 years, I don't know.
"But when a person represents so much to a club and when a club represents so much to a person, and that's the case, I think he has to be back one day."
Meanwhile, Mourinho continues to seethe about events at Aston Villa on Saturday, when he, along with Willian and Ramires, was sent off by referee Chris Foy.
Asked if he had spoken to Ramires about the shocking challenge on Karim El Ahmadi, Mourinho shifted the blame to Foy.
He said: "I feel that what happened on minute 92 was a consequence of the other 92 minutes that we played before that.
"If you want to ask you should ask about what made that tackle happen."
Asked specifically what he was referring to, he said: "Everything that happened. I bring the game into disrepute. I cannot."
Mourinho's dismissal was his second of the season.
He was fined £8,000 by the Football Association following his touchline dismissal against Cardiff in October.
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