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].”