The Blues could be drawn against Gala in the knockout stages and the Portuguese would welcome "King Didier" back to west London with open arms
Both sides qualified for the last 16 on Wednesday, setting up a potentially emotional Blues reunion for the Ivorian, who spent eight years with the west London outfit.
The striker - signed by Mourinho in 2004 - went on to become a Chelsea legend, scoring 157 goals in 341 matches, making him their fourth-highest scorer.
In his final game for the Blues, Drogba scored an 88th-minute equaliser in the 2012 Champions League final against Bayern Munich, setting up a penalty shootout that he eventually finished with the decisive spot kick.
When asked by reporters about the potential of playing the Turkish giants on Wednesday, Mourinho replied: "Yes, Galatasaray is difficult. The Turkish champions with 'King Didier'. Very difficult.
"But I'd like Didier to be back here and feel what I felt. He deserves to come here and get the reception double or three times better and bigger than I had [when I returned with Inter]."