Drogba, who helped Chelsea win the European title last season by scoring the winning penalty in the final shoot-out against Bayern Munich, joined Gala in January on a one-and-a-half year deal following an ill-fated spell at Chinese side Shanghai Shenhua.
If he does play, the 34-year-old striker looks set to link up with the Turkish side's other major transfer window signing - Holland midfielder Wesley Sneijder.
Galatasaray coach Fatih Terim admitted last Friday's 2-1 win over Akhisar Belediyespor and Drogba opening his goalscoring account was the perfect preparation for the return to European action.
"It gave us a morale boost ahead of the Schalke game," Terim said.
"When he is fit, Drogba has the ability both to keep the ball for us up front and to lead the team.
"When you add Sneijder to that, we will perform much better. Both have integrated with the team very quickly."
Along with Drogba, Sneijder adds experience of European success to Galatasaray. He was part of the Inter Milan side who completed a Champions League, Serie A and Italian Cup treble in 2010.
Gala will face Bundesliga side Schalke, who have managed only one win in their last 12 games since they beat Olympiacos back in November.
Schalke midfielder Marco Hoger knows a tough test awaits his team in Istanbul, but while they respect Gala, they do not fear them.
Hoger told the club's official website: "Fear is always a bad advisor.
"Galatasaray has great players like Didier Drogba, Wesley Sneijder and some more. Respect is of course there but we fear no one."
However, Schalke look set to receive a boost as Dutch striker Klaas Jan Huntelaar looks likely to return after struggling with an eye injury in recent matches.
"We also have good players in our ranks," Hoger said.
"The fact that Huntelaar is fit again is important. In the current Champions League season, he has already achieved some great results.
"We all hope that he keeps it up in Istanbul."
Schalke will be without several other key players, with Kyriakos Papadopoulos, Atsuto Uchida, Ibrahim Afellay and Ciprian Marica all missing out.
Gala, meanwhile, will be without Tomas Ujfalusi and Johan Elmander due to injury but Emmanuel Eboue could return at right-back.