The runaway Premier League leaders visit Atletico in the first leg of their Champions League last-16 tie on Tuesday, as they return to the scene of their victory in last year's final.
Atletico are struggling in La Liga, with just one win in their last seven games, but Klopp remains wary of the match-up.
"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 the Mirror.
"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."
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 now 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."