The 22-year-old says he is relishing the prospect of facing a side who boast the world's finest coach and stars like Cristiano Ronaldo and Mesut Ozil
Jurgen Klopp's side took four points from los Blancos during the group stages and, while he feels Jose Mourinho's men have improved since then, the Germany international has stressed his side will have no fear ahead of the encounter.
"[Madrid] is one of the best clubs in the world. I think they're the best team in the Champions League, but we have beaten them in the group before," he told AS.
"Undoubtedly Madrid are now better than they were in the group, but at we showed we could beat anyone and that leaves us with a positive feeling.
"Reaching the semi-finals of the Champions League is very important for Dortmund. In fact, nobody had marked us as favourites to reach the second round because of the group we had with Real Madrid and Manchester City. The work we have done has been perfect.
"We are not worried about playing against Real Madrid. Whatever happens we will try with all our might to reach the Champions League final on May 25."
Gundogan went on to reveal his admiration for Blancos boss Jose Mourinho, and stated he is relishing the prospect of playing against who he believes to be the world's best two players: Cristiano Ronaldo, and Mesut Ozil.
"There is no question that Madrid has a lot of quality in midfield. But most important for me is that it has the best coach in the world," he added.
"I feel happiness [at the thought of playing against Ronaldo and Ozil]. Those two are the best in the world. Three years ago I saw them both on television and now I have the opportunity to play and share the same field against them. It's a unique feeling."