Before moving to Anfield in October 2015, the German coach was in charge of Borussia Dortmund for seven years, during which he guided the club to the final of the competition in the 2012-13 season.
Liverpool are on their way to the last-16 stage, having secured a 7-0 victory over Spartak Moscow at Anfield on Wednesday night.
The scoreline racked up the team's group-stage total of goals to 21, which is the most that any English club has scored in this phase of the competition.
As a result of Liverpool topping Group E, they could now draw Basel, Bayern Munich, Juventus, Shakhtar Donetsk, Porto or Real Madrid.
"Nobody could imagine that it would go like this tonight," Klopp told BT Sport. "It was an all or nothing game for both teams. Spartak Moscow is a really good side, I know you won't think so now but they are difficult to play against. We opened the game perfectly and after we took the lead we didn't have to defend. It was a nice night at Anfield.
"It helps to get an early goal or two. I told them at half-time we needed to show that we learn from our mistakes and keep going. It's really difficult when we go to the next gear and use the space, it was nice to watch tonight.
"I have nothing to moan about tonight, it's all good. We changed the system a little bit, the boys did it really well. The defence was spot on, I really liked it.
"I don't mind too much who we get - usually I always get Real Madrid so we will see. We have no preferred opponents, it will be really nice after a long time. I love this kind of news."
All five Premier League teams have made it into the next round.