Simeone darted down the tunnel at the final whistle without any acknowledgement for his opposite number a fortnight ago when Liverpool beat his side 3-2 at the Wanda Metropolitano.
And in the build-up to the return fixture at Anfield, the Argentine said that he doesn't agree with mandatory handshakes after games with emotions running high for both coaches at the end of matches.
"I don't like the greeting after the match because they are the emotions of two sides in different emotional minds," he said.
"I know in the UK it is a custom and a sign of respect but I don't share it and I don't like the falseness it may include so I behave how I feel.
"I don't know Klopp as a person very well but I know he is a great coach who has done great work at every club he has been at."
Klopp was asked Simeone's snub after the game in Madrid, but says he's not bothered about shaking the Argentinian's hand after the match at Anfield now he's aware of his stance.
"I respect him a lot," said Klopp.
"We don't know each other but I respect what he is doing at Atletico, absolutely exceptional against strong sides year after year. Really impressive.
"The handshake? If I knew he doesn't do it, then I wouldn't try it.
"We were both emotional [after the game in Madrid] but now I know he doesn't like to do it, so no problem.
"Then we can all go home happy but between the handshakes, it's an important game, which I am more concerned about."
This will be the fourth meeting in three seasons between the two sides and the last couple, Liverpool's thrilling win a fortnight ago and Atleti's Anfield victory in March 2020 which knocked out the holders, have had all the elements of a great modern-day rivalry.
Atletico's former Burnley and Tottenham full-back Kieran Trippier insists they head to Anfield looking for the victory which will cut their hosts' five-point lead in Group B.
"We don't go into any game to try to go for the draw. We want to win, we have that winning mentality at this club," said the England international.
"We go there full of confidence, we have this fantastic squad.
"We showed character, the fight and desire last year to beat Liverpool and it will be no different.
"We go there tomorrow with the same winning mentality to get the three points."