The pair were paired together in Monday’s draw in Nyon, Switzerland, with the first leg taking place at the Wanda Metropolitano stadium on February 18.
The game will mark a return to the setting of Liverpool’s Champions League triumph in June, when a 2-0 win over Tottenham Hotspurs secured a sixth European crown.
While Klopp is wary of the enormous nature of the task ahead, he does not believe Simeone will be too pleased facing the European champions at this stage either.
"It's an interesting draw," Klopp told his club's official website.
"Before the draw, I actually thought it would be Madrid - either one of the two clubs - and that's the way it is.
"Madrid is the place where we only have fantastic memories, all of us, so that's great, but this time we play Atletico there and it's their home ground.
"It's a tough one, but if you go through all of the draws, there are pretty much four or five potential finals already in the last 16.
"So, really, really good; a good draw, a difficult game like it should be, but I don't think Mr Simeone is running through his living room and is happy that he got Liverpool.
"It will be a tough game. Two teams who are used to playing intense football. Different styles and slightly different organisation, of course, but both are ready for intensity and that makes it pretty tough for both."
