Spanish giants Real won 3-0 at Santiago Bernabeu last week to take a giant stride towards the semi-finals of the UEFA Champions League.
Dortmund go into the second leg of the last-eight clash with a mountain to climb, but their chances of pulling off a stunning comeback are enhanced by the return of talismanic striker Robert Lewandowski.
The Poland international missed the first leg due to suspension, but is set to line up against Carlo Ancelotti's side in what could be his last European game for the club. Lewandowski will join Bayern Munich at the end of the season.
Lewandowski scored all four goals when Dortmund beat Real 4-1 at home in the semi-final first leg last season and the Bundesliga side could do with more heroics from him on Tuesday.
And Klopp has vowed to go all out for a stunning victory at Signal-Iduna Park, pointing to recent comebacks against the likes of Stuttgart and Wolfsburg as proof they have the character to get back into the tie.
He said at a press conference on Monday: "The line-up will be slightly different than in Madrid, and we will try our hardest against this very strong team
"We will give everything tomorrow and show the fans what they deserve, a passionate performance from Borussia Dortmund
"Last year, we went out in the final. This year it looks like the quarter-finals. But it is not over yet.
"As we are specialists in second halves at the moment, which is tomorrow... the second half of the quarter-finals.
"Real Madrid are one of the favourites to win the the Champions League. We want to defend better and use our chances better than in Madrid."
Klopp added that goalkeeper Roman Weidenfeller (arm) should be fit, but Nuri Sahin (back) is an injury concern and Sebastian Kehl is suspended.
