The 45-year-old has stressed the Blancos are not an option for him at the moment, while also taking the time to discuss Nuri Sahin's future
The 45-year-old is reportedly one of the candidates to replace Jose Mourinho once the Portuguese leaves the club, and Klopp was one of the fans' favourites for the job in a recent survey among Madrid fans.
"Perhaps the Madrid fans want a German coach again. However, I don't have time for Real Madrid at the moment," Klopp was quoted as saying by Bild.
"It shows that a lot of people have seen our matches against Real Madrid [in the Champions League] and that they liked the way we played. There's worse things that could happen..."
The BVB coach also had his say on the ongoing rumours linking Liverpool loanee Nuri Sahin with a return to the reigning Bundesliga champions.
"I cannot really say anything about it at the moment. It's not a secret that I have regular contact with Nuri. We will have to wait and see what he does, though.
"Nuri is a great player, but he was injured when he joined Real Madrid. That was his problem.
"I don't know what Liverpool manager Brendan Rodgers plans to do with him. However, fielding him in the No.10 position is not the best solution in my opinion."
Sahin has made only seven Premier League appearances since joining Liverpool on loan from Blancos.