The 50-year-old German tactician also claimed Pep Guardiola's men did not want to face them in the continental clash, given his "not-too-bad" record against them.
League leaders City have been beaten only once in the ongoing season and the defeat came against Liverpool at Anfield in January. Also, Klopp has tasted success five times in nine games as a manager against the Citizens, losing only two of those ties.
The Liverpool boss even suggested that City director of football Txiki Begiristain was not amused when the quarter-final draw, announced Friday, March 16, in Nyon, pitted the two Premier League clubs against each other.
"It is cool. For sure, the first one will be a really exciting game to watch. I love these games. They are fantastic for me as a manager and you know if you play City they do what they do at the highest level. They don't defend the result, they go again," Klopp was quoted as saying by Liverpool Echo.
"If we can put our specific style, philosophy and mix it up with our attitude and stuff like this, being brave, then there is something in it for us," he added.
"They [City] didn't want us. We all know about that. Our record is not too bad against City. Yes, it was a close game here and stuff like that.
"We are not the team they love to play constantly, let me say it like this.
"But are we their nightmare? No, I don't think so. When you think about the draw, the team around the corner you can go by bus, you don't want it. Everybody is a little like this."
Klopp laments league scheduling
Meanwhile, Klopp also lamented the league fixtures that see them playing a big derby match between the first and the second legs of the Champions League quarter-finals. The Reds visit Everton for their league clash at 12:30 pm BST April 7, less than 64 hours after the Anfield meeting against City.
Guardiola's men have a packed schedule as well, as they take on cross-town rivals Manchester United April 7.
City, who are eyeing their first-ever Champions League win, however do not need to fret over the Manchester derby, given they are favorites to win the league title. On the other hand, Liverpool, who are sitting on the fourth spot with 60 points, will be battling to finish among the top four.
"So, a really intense game and you give us the worst moment for a game against Everton, which we cannot say to our supporters 'I know it is Everton but we play on Tuesday again'," Klopp said.
"What's that? If we had Tuesday-Wednesday [it would have been fine] but no, we have the Wednesday-Tuesday rhythm. In between, Everton. Right!
"When we play Everton, they play United. Maybe they are not concentrating [too much on] that game because then they can be champions a week later and Man United can win a game at Manchester City which would not help us as well."