The Bundesliga outfit were drawn against the Spanish giants in the knockout rounds for the second year in succession, after their semi-final meeting last season.
Dortmund were victorious in that tie, Robert Lewandowski inspiring them to a 4-1 first-leg win before they held on nervously at the Bernabeu, losing 2-0 to progress 4-3 on aggregate.
It was the second time the Germans had got the better of Madrid last season, after taking four points off them in the group stages of the competition, and Klopp stressed his belief that the cream always rises to the top in the Champions League.
"It's a good draw," he told the club's official website. "If you repeatedly qualify for the round of the last eight teams in Europe, you just have to expect that there are just more frequent pairings - as in this case.
"We're thrilled with this challenge and will try to use our small chance. The fact we play first in Madrid, can be an advantage.
"It is certainly not the time now to raise the white flag."
However, chief executive Hans-Joachim Watzke admitted he would have liked a bit of variety.
"I would have liked a different team for a change," he is quoted as saying by UEFA.com. "We played Madrid four times last year! However, we are still looking forward to it."
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
