Draxler helped Schalke to a 2-0 victory over Frankfurt on Friday, a result that moved Jens Keller's men level on points with second-placed Dortmund in the Bundesliga table.
A Bayern victory in Der Klassiker on Saturday would significantly aid Schalke's hopes of beating Dortmund to second and securing automatic qualification for next season's UEFA Champions League.
"We want to finish ahead of Dortmund but we'll see what happens," Draxler said. "I'm supporting Bayern, though."
Both of Schalke's goals against Frankfurt came in the second half, with Max Meyer scoring shortly before the hour mark and Jefferson Farfan adding a second in injury time.
Draxler believes the Gelschenkirchen outfit were rewarded for a strong second-half showing.
He added: "We were too slow in the first half, and we said at half-time that we couldn't keep playing like that. The second half was much better from us."
