The Reds face their second clash with City in seven days on Saturday, with the two sides meeting at Wembley for their FA Cup semi-final.
It is a tie that has proved controversial given the travel issues both sets of fans will face, but it promises to be another high-quality game between the two best sides in world football.
Last week at the Etihad, Liverpool fought back for a 2-2 draw that kept their title hopes alive, but they were far from their most fluent.
In his pre-match press conference on Thursday, Klopp acknowledged that “a couple of positions” in particular struggled, calling for a much better performance in London.
“We all think a lot about these kinds of games. We have to,” he told reporters.
“I think City were really strong last week and we were not at our best. So I would like to see a game where we are at our best as well.
“It would be interesting, so let’s give it a try – that would be a surprise, all of a sudden we are good!
“The boys did a lot of good stuff in the game, but I really think in a couple of positions we are able to perform on a completely different level.
“I think we should give that a try.”
Unlike last time out, which was billed as a winner-takes-all clash that ended with a share of the points, only one side can emerge from Saturday with a place in the FA Cup final.
“It’s a cup game, a one-off, which means if it’s 2-2 again it’s 120 minutes, then if it stays there 2-2 then it goes to a penalty shootout,” he continued.
“It’s crazy, that would be really crazy if we have to go all the way.
“But honestly, I really like that. I want to have 12 games from now until the end of the season, we want to be in the finals.
“It’s not about that, it’s just tough and it doesn’t make it easier.
“But it’s still the best schedule to have because it means you are in all competitions as long as somehow possible. That’s why I’m really looking forward to the game.
“Wembley is a big pitch, so we have to cover a lot of grass, to run a lot, to close big gaps and all these kinds of things.
“But I think it will be cool. Of course, both teams will use the last game for analysis – we will see who used it better.”