Liverpool's Champions League last-16 visit to Atletico Madrid tomorrow evening represents the first time the two managers have ever gone head to head in any competition.
Both have built their reputations on taking unfancied sides to major honours without matching the big spending of many of their rivals at home and abroad.
And that has led to a mutual respect and a regular exchange of messages, according to Klopp.
The German explained: "People say about me that I am emotional on the sideline, so if I am on level four, then I would say Diego is on level 12 or so! Really, I am like the Kindergarten Cop against him!
"It’s really impressive, over all these years. Eight years, that’s really long and having still this emotional level, wow - that’s absolutely impressive.
"As I say, his teams are always world-class organised, so that makes him one of the best.
"We’ve met once or twice, we exchanged some messages after big defeats or big wins and tomorrow in a real competitive game we will meet for the first time and it will be interesting, absolutely interesting."
With his side locked in a battle for Champions League qualification rather than the title, and having suffered Copa del Rey humiliation at the hands of lowly Cultural Leonesa, Simeone is currently enduring one of the most difficult seasons of his Atleti tenure.
But Klopp believes the Spaniards still represent a massive threat and is under no illusions as to how difficult it will be for Liverpool to reach the next round.
He added: "Playing Atletico is one of the most difficult things in the life of a football player.
"[They are] really good organised, a result-machine, squeezing results pretty much out of each game if possible. Yes, people will tell me – and have told me already – this year it is not exactly like it was, it’s a transition period that’s normal, but still [they are] fighting with all they have, don’t [concede] a lot of chances and all that stuff. That is really difficult.
"What they played so far in the season was not as bad as people are saying and it is nothing to do with their chances tomorrow.
"The team who will play better tomorrow and then in the next game when we play against each other, who fight more, who want it more will go to the next round and not the team who plays a better Premier League or La Liga season. It’s as easy as that.
"We are here and I think nobody doubts that we are really ambitious, so we will give it a proper try."