The Reds are tasked with stopping their opponents' European dominance when locking horns in Kiev next weekend, facing the back-to-back winners of the competition.
Madrid have triumphed three times in the last four years and are way out in front in terms of European honours, but Klopp has pointed out that Liverpool also have a proud history on the continent, even if their most recent success came 13 years ago when famously overturning a three-goal deficit against AC Milan.
"Yes they are favourites, they know everything, they can write their own scripts because they have now experienced it four times in the last five years," he is quoted as saying by The Guardian. "There have been three dominant clubs in the last few years, and we are facing one of them.
"I have no problem with the situation and I don't feel like an underdog. Liverpool were absolutely not favourites in 2005, and that was before they went 3-0 down.
"To be honest, we like the role we are in. We like the situation and we are in a good moment. Real Madrid are a side of the highest quality going for three wins in three years, but we are Liverpool. That's something not to forget."
Liverpool have spent time training in Marbella this week in preparation for next Saturday's showdown in Kiev.