The Gelsenkirchen club believe the Cote d’Ivoire international is not properly registered to play in the European competition for Fatih Terim’s side.
Fifa ratified the switch from Shanghai Shenhua despite the Chinese club’s protests, but it is possible their last-16 German opponents are protesting over a separate licence-to-play issue.
"There are doubts about the validity of the permission to play for Drogba in the Champions League," the Bundesliga club announced on their official Twitter account.
"Schalke reserves its rights and is looking into this."
The former Chelsea striker joined Galatasaray on an 18-month contract in the last few days of the January transfer window, leaving Shanghai Shenhua on a free transfer as they had been deemed not to have paid his wages.
Schalke general manager Horst Heldt claimed on Thursday "it would be irresponsible not to do this [launch an appeal]."
Drogba did not have much of an effect on the scoreline on Wednesday as Burak Yilmaz's opening goal was cancelled out by Jermaine Jones' equaliser, and the two teams fought the remainder of the match on level terms.