Leverkusen and Stuttgart are the two favourites to win the cup this year, with both Bayern Munich and Borussia Dortmund already out of the running.
Xabi Alonso's Leverkusen are currently four points clear at the top of the Bundesliga, while surprise packages Stuttgart are in third.
The two held each other to a high-quality 1-1 draw in the league on Sunday, just hours before they were drawn against each other once again in the cup.
"It's a shame, because this would have been the ideal pairing for the final," former Leverkusen cup-winner Martin Klee told ARD broadcaster.
Stuttgart knocked out Dortmund in the round of 16, while Leverkusen have cruised to the quarter-finals with three wins against lower-league opposition.
The quarter-finals are set to be held on January 30 and 31 and February 6 and 7, at a time when both clubs are expected to lose key players to international duty during the Africa Cup of Nations.
Stuttgart striker Serhou Guirassy is likely to be called up for Guinea, while Leverkusen could be without Nigeria's Victor Boniface, Burkina Faso's Edmond Tapsoba and Morocco's Amine Adli.
In the other quarter-finals, St. Pauli host Fortuna Duesseldorf while Kaiserslautern travel to Hertha Berlin.
Serial giant-killers Saarbruecken will be hoping to claim a third top-flight scalp when they face Borussia Moenchengladbach.
Third-tier side Saarbruecken have already sensationally knocked out both Bayern Munich and Eintracht Frankfurt, and will be hoping to reach the semi-finals for the second time in four years.
"Our vice-president predicted we would get Gladbach, and that's how it has turned out," said sporting director Juergen Luginger.
