Liverpool topped their group ahead of Napoli and their bid for a second consecutive European crown takes them back to the Wanda Metropolitano - the scene of last season's final - to face dangerous LaLiga giants Atleti.
Klopp suggested he anticipated a return to Madrid, while recognition of a testing fixture was tempered by the strength of a last-16 draw containing only clubs from Europe's 'top five' leagues.
"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."
Reflecting on the draw as a whole, which saw Premier League rivals Manchester City paired with 13-time champions Real Madrid, Klopp added: "I think I said last time that it is somehow the strongest ever last 16 or last eight, but it looks like it becomes stronger and stronger every year."