Defeats to Lazio and Anzhi Makhachkala saw their respective European campaigns end in the last-32.
As things stand, Gladbach are three points adrift of the top six with Hannover a further point in their wake, making victory paramount for both sides at the Borussia Park Stadion on Sunday.
"We have still got to play a lot of sides at the same level as us and Hannover are one of them," said Gladbach coach Lucien Favre.
"They are a dangerous side who have great potential, above all in attack.
"They have not lost any important player for three years, yet they have added many interesting new faces.
"There can be no doubt about it - Hannover are a very good team."
Hannover have proven their credentials by qualifying for Europe in each of the past two seasons and their coach Mirko Slomka has made no secret of his desire to be back again next term.
"We want to be looking at the screen to see if we get a good draw ourselves," he said after watching the draws for the quarter-finals of the Champions League and Europa League immediately prior to a press conference on Friday.
"That is why it is important for us to aim for three points (in Gladbach)."
Revenge is also on the Reds' minds after losing the reverse fixture, despite leading the game 2-0.
"That really hurt and maybe that will give us some extra motivation to win something back," added Slomka.