The German manager believes he and his Argentine counterpart have battled for little reward in years gone by
The Premier League leaders visit Atletico in the first leg of their Champions League last-16 tie on Tuesday.
Liverpool return to the scene of their victory in last year’s final, and they are preparing to face an Atletico side that are struggling.
But Klopp remains wary of Simeone and Atletico, who have just one win from their past seven games in all competitions.
“Their goal difference [in La Liga] is they have scored only 25 which is not too many, but have conceded only 17, which is low,” Klopp told UK newspapers.
“They have had massive injury problems in recent weeks, a lot of strikers missing. But [Alvaro] Morata was on the bench [against Valencia on Friday], I’ve heard [Diego] Costa is back in training and Joao Felix is available I’m pretty sure.
“If somebody can play for a result, it’s Atletico. Mr Simeone, who I respect a lot, he tries everything.
“We have a similar story a little bit. We tried a lot and didn’t win, but we still tried. I like that. He is so competitive – wow! Actually, we have a good relationship but I’m pretty sure he will forget that on the touchline because he is so animated.”
While facing Atletico away shapes as being tricky, the Wanda Metropolitano will bring back happy memories for Liverpool after their win over Tottenham in last year’s final.
But Klopp said his side – who are 25 points clear atop the Premier League – were focused on their task.
“We know that it’s just a stadium, but it’s a positive emotion that we have when we think about that stadium,” he said.
“It was one of our greatest nights and I’m pretty sure that when the boys will go in they will see it.
“But we are not going there for a pilgrimage. For sure not. We have had enough time to let these things settle.”