Klopp's side knocked out Real at the semi-final stage last season, but Klopp is worried that Carlo Ancelotti's men will be able to build a convincing lead at the Santiago Bernabeu before the second match in Dortmund.
"Playing the second leg at home may be a slight advantage but I fear Madrid trying to settle the tie here," the German told reporters. "I have seen many of their games and they never finish a match without one scoring opportunity.
"They have incredible quality and we can't ignore that. If we play our game and keep our heads up, we will have chances."