The Reds hosts Niko Kovac's side today in the first leg of their Champions League last-16 tie, FourFourTwo reported.
Liverpool has been tipped by many as the favorite to progress to the quarterfinals, with Bayern's dominance of German football appearing to be weakening during something of a transitional season.
The German giant sits two points behind Bundesliga leader Borussia Dortmund, having played a game more, and twice fought back from a goal down to beat Augsburg 3-2 on Friday.
Klopp, though, thinks Bayern's improved results since a run of no wins in four games in September shows it will be a real threat at Anfield.
"After six years as the dominator of the league, it was clear this would be a more difficult year," he said. "They are two points behind Dortmund, they play Dortmund at home, they're in the cup [DFB-Pokal], in the Champions League last 16... It's a completely normal situation.
"With a huge quality team, you need to have the desire of a newcomer combined with the quality of a real contender. Maybe in the beginning of the season they didn't have that but the situation from my point of view makes them even more dangerous than before.
"We cannot have the same target as Bayern because they are six times in a row the champions, they want to make history with a seventh. Our history would be completely different. Maybe we achieved a little bit more than people expected so far but both are in a similar situation.
"It's a long way to go but we don't have to think about the league, just the Champions League. If I wasn't involved, I would buy a ticket."
Today's game sees Klopp come up against Mats Hummels and Robert Lewandowski, who were key figures in his Dortmund side that won back-to-back league titles in 2011 and 2012.
"I worked together with these boys. Two fantastic players. I have to be really thankful – without them probably my career would not be the same," he said.
"We all benefited from each other. That's part of my life and part of my history. We'll always have a lot of respect for each other.
"I know a lot about them. I really like them. We will try everything to, what can I say? To let them not shine."
Liverpool finished second to Paris Saint-Germain in the group, meaning it must play the home leg of the tie first, but Klopp does not consider that to be a disadvantage.
"When two good teams face each other, it is not decided in one game," he said. "We have two legs to play and we will be 100 percent focused on both of them. It's difficult but it's possible and that's all I need."