Dortmund beat Los Blancos in the semi-finals of the competition last season, but Klopp believes that the Spanish side are stronger this time around.
"Real Madrid are the favourites. With our budget and our injury list there is no doubt we are the underdog of the tie," Klopp told reporters at a press conference.
"They have bought good players like Gareth Bale and Isco. They have tremendous strength in all areas and are a very complete team."
The first leg takes place at the Bernabeu on Wednesday.