The hosts are fifth in 2. Bundesliga at present, having reached the quarter-finals of this competition last season.
Match preview
Indeed, Hannover enjoyed their best run in the DFB-Pokal for 15 years before being dumped out by eventual champions RB Leipzig with a 4-0 defeat in the last eight last season.
Die Roten eliminated Borussia Monchengladbach 3-0 at Niedersachsenstadion in the third round of their route to the quarter-finals, so they clearly have pedigree when it comes to knocking out Bundesliga sides ahead of hosting Dortmund on Wednesday.
Their only ever DFB-Pokal triumph came as a second tier side in the 1991-92 season, too, when they defeated Gladbach 4-3 after extra-time in the final. While that seems unthinkable in modern football, it only takes a few upsets for the draw to open up in any knockout competition.
Having finished in the bottom half of 2. Bundesliga in each of the last two seasons, former Greuther Furth boss Stefan Leitl has been tasked with restoring Hannover's top-flight status, as he managed with Furth during his three-year spell at the club.
20 points from his first 12 league games in charge has helped them climb to fifth position in the table, although they are five points adrift of the three promotion places on offer and have some work to do to make up that ground. While that will be Leitl's priority, a famous cup win in midweek would undoubtedly lift spirits at the club.
Dortmund could use a win themselves, though, having fallen seven points behind league leaders Union Berlin after a 2-0 loss away to Urs Fischer's side on Sunday.
Goalkeeper Gregor Kobel's dreadful error allowed Janik Haberer to pounce on the loose ball and break the deadlock after only eight minutes, before the midfielder beat Kobel from distance to double the hosts' lead 13 minutes later.
More than perhaps any other team in European football on current form, Union Berlin are not a side to fall behind against, with their counter-attacking style and disciplined defensive organisation making them incredibly difficult to overturn a deficit against.
Head coach Edin Terzic will be demanding a faster start from his players in Hanover on Wednesday, especially as the 39-year-old can ill afford being eliminated from the tournament which represents his team's most realistic chance of winning this season.
Having won the DFB-Pokal as interim head coach at Dortmund two seasons ago, Terzic clearly knows what it takes to win this competition, as BVB attempt to join Werder Bremen on six all-time German cup triumphs in behind Bayern Munich's unassailable tally of 20.
Hannover DFB-Pokal form:
W
Hannover form (all competitions):
W
D
W
L
L
W
Borussia Dortmund DFB-Pokal form:
W
Borussia Dortmund form (all competitions):
W
L
W
D
D
L
Team News
Hannover look likely to be without Sebastien Ernst due to an Achilles tendon injury, while Cedric Teuchert is doubtful due to a muscle strain.
Maximilian Beier is likely to replace Teuchert in attack should the 25-year-old miss out as expected, although Leitl may opt to bring another defender or midfielder into the side in order to shore his team up out of possession.
Dortmund, meanwhile, are expected to travel without Mateu Morey, Mahmoud Dahoud, Jamie Bynoe-Gittens and Anthony Modeste due to injury concerns, while Sebastien Haller is still unavailable due to a testicular tumour.
Terzic may look to make as many changes as he can while keeping his team competitive on Wednesday, with club captain Marco Reus set to make his first start since sustaining an ankle injury in the Revierderby last month.
Hannover possible starting lineup:
Zieler; Muroya, Neumann, Borner, Kohn; Leopold, Kunze, Shaub, Kerk; Nielsen, Beier
Borussia Dortmund possible starting lineup:
Kobel; Wolf, Sule, Schlotterbeck, Rothe; Ozcan; Reyna, Brandt, Reus, Hazard; Malen
We say: Hannover 0-2 Borussia Dortmund
Hannover are only 15 places below BVB in the German footballing pyramid heading into the encounter, so they will be confident of making their more illustrious opponents work hard for their victory.
However, we expect Dortmund to bounce back with a win on Wednesday, with the return of Reus likely to provide them with a huge boost.