They have a poor record against Saturday's opponents, too, having not beaten Dortmund in their last four meetings in all competitions.
If last season's Bundesliga runners-up are to return to winning ways they are likely to have to do so without a number of established first-team players.
Marco Reus was ruled out of international duty with a torn ankle ligament and is a doubt, while Nuri Sahin is also set to miss out with a similar injury.
Klopp will also be without the suspended Mats Hummels as well as long-term injury worries Marcel Schmelzer (thigh), Lukasz Piszczek (hip and groin) and Ilkay Gundogan (back).
However, Sven Bender could make a return from the groin and back injuries that forced him to miss Germany's final two Fifa World Cup qualifiers.
None of the trio featured in Dortmund's practice match against Cologne on Tuesday, which saw Pierre-Emerick Aubameyang and Julian Schieber score in a 2-1 win.
Hannover have injury concerns of their own, with striker Mame Biram Diouf a doubt due to a hamstring tear that kept him out out the 1-1 draw with Hertha Berlin and Senegal's 3-1 defeat to the Ivory Coast on Saturday.
Striker Didier Ya Konan (ankle) and defender Felipe (hip) are also ruled out, having undergone operations on their respective injuries.
Mirko Slomka's men kept themselves sharp during the international break with a 16-1 friendly win over lower-league side TSV Barsinghausen and will need to take some of that finishing ability into Saturday's game.
While Hannover have conceded just 11 goals in the league, they have also only scored 11 - the lowest of any team in the top eight.
Slomka's men will see Dortmund striker Robert Lewandowksi as a major threat, with the Poland international having scored six times in the Bundesliga this season, and seven in his last four against Hannover.