Leverkusen take on their second division opponents having eliminated Bayern Munich in the last 16. Borussia Dortmund and Eintracht Frankfurt, both five-time winners, have already been eliminated.
RB Leipzig, winners of two of the past three German Cups, will play at home against 2015 champions Wolfsburg. Leipzig have never lost a German Cup quarter-final, winning four from four.
Six-time winners Werder Bremen, who have more German Cups than any other team besides 20-time winners Bayern, play at third-tier Arminia Bielefeld.
Three-time winners Stuttgart will host Augsburg in the final last-eight clash.
Located just 15 kilometres away along the Rhine, Leverkusen and Cologne's rivalry has become increasingly bitter in recent seasons.
Cologne blame Leverkusen for breaking a 'gentleman's agreement' between the clubs not to sign junior players from each other, when Bayer poached a then 17-year-old Florian Wirtz, now a Germany regular.
In 2022, Cologne fans cheered as Wirtz was stretchered off with a torn ACL in a match between the sides.
In May 2024, Leverkusen fans, fresh from winning a first-ever top-flight title, held up banners celebrating Cologne's relegation to the second division.
The German Cup final will be held on May 24 at Berlin's Olympic Stadium.