Bayern booked their place in the last eight with victory over Arsenal while Dortmund seem set to follow them on Wednesday night when they defend a 4-2 lead from the first leg against Zenit St Petersburg.
The two German rivals met in the Wembley final last May, Bayern emerging 2-1 victors thanks to a late Arjen Robben winner, and Weidenfeller would rather not face Pep Guardiola's men until later in the tournament again this time.
"It's a European competition and we could do without an all-German duel, for as long as it's possible," he told Kicker magazine.
The Germany international would also like to avoid Barcelona in the next round, although he admits he would like to face the Spanish giants at some point in the future.
Before that, he fancies Olympiacos, should they get the better of Manchester United.
"I've never played against Barcelona before and that would be a huge challenge, to play at the Nou Camp," Weidenfeller said.
"I would like that experience, although not necessarily in the quarter-finals.
"Olympiakos would be something. The last time we played in Piraeus, we didn't look very good so we definitely have something to put right there."
Dortmund will now be focusing much of their attention on the Champions League after seeing their hopes of catching Bayern at the top of the Bundesliga practically ended by Saturday's home defeat to Borussia Monchengladbach.
Bayern can clinch the title next weekend against Mainz if Dortmund and local rivals Schalke fail to win their next Bundesliga fixtures.
Dortmund are also into the semi-finals of the DFB-Pokal, where they face Wolfsburg on April 15.