Both sides have won this competition three times each in their history, although neither have lifted it since the 1990s, so they would certainly welcome the opportunity to do so once again.
After performing above expectations to currently occupy 10th place in their first season back in the Bundesliga, a cup run would add major gloss onto what looks like being an exceptional season for Stuttgart.
Pellegrino Matarazzo's side earned their first home win of the season in a 2-0 win against struggling Mainz 05 on Sunday, with Nicolas Gonzalez and Silas Wamangituka highlighting their burgeoning talents as two of the brightest young attackers in European football with a goal apiece.
With survival all but secured this season and a push for Champions League football surely beyond them, Matarazzo will be tempted to go full strength against Gladbach on Wednesday as Stuttgart look to secure their first trophy since winning the Bundesliga in 2007.
The club last won the German cup in 1997, having finished as runners-up in 2007 and 2013, with a narrow 1-0 win over in-form Freiburg in the last round showing they mean business this time around.
Gladbach, meanwhile, have not won a trophy since last lifting the DFB-Pokal for the third time in 1995.
With the rumours of Marco Rose departing for Borussia Dortmund in the summer unlikely to go away anytime soon, the 44-year-old would dearly love to provide the club he has given so much to with a tangible trophy should he leave for pastures new at the end of the season.
Qualifying for the Champions League last season, of course, was arguably a bigger and more important achievement for Gladbach, with finishing within those top four places in the Bundesliga remaining a priority for them this season.
However, Rose has ample squad depth to rest a few key players while still selecting a team strong enough to beat Stuttgart on the day.
Stuttgart DFB-Pokal form: WW
Stuttgart form (all competitions): LWDLLW
Borussia Monchengladbach DFB-Pokal form: WW
Borussia Monchengladbach form (all competitions): WWDWWD
Sasa Kalajdzic started and scored in the weekend's win over Mainz so could receive another opportunity to showcase his credentials for a more permanent position in Matarazzo's starting XI.
Gladbach, meanwhile, are likely to make several changes, with Florian Neuhaus and Lars Stindl coming into the team after only being used from the substitutes' bench in Saturday's 1-1 draw at Union Berlin.
Stuttgart possible starting lineup:
Bredlow; Stenzel, Anton, Kempf; Coulibaly, Karazor, Mangala, Thommy; Didavi, Klimowicz; Kalajdzic
Borussia Monchengladbach possible starting lineup:
Sippel; Lainer, Ginter, Elvedi, Wendt; Neuhaus, Kramer; Wolf, Stindl, Herrmann; Embolo
We say: Stuttgart 1-2 Borussia Monchengladbach
Stuttgart have struggled at home this season, with Gladbach's ability in transition likely to cause them significant problems.
The winner could come down to which manager makes the fewest changes, with Gladbach possessing greater strength in depth to cope with Rose's usual rotation policy.