The two domestic rivals meet at Anfield in the first leg of their quarter-final tie on Wednesday, with the return fixture taking place at the Etihad Stadium the following Tuesday.
On the brink of securing the Premier League title and having already won the Carabao Cup, City have the chance to complete a famous treble if they go on to conquer Europe this season.
However, Liverpool remain the only side to beat the champions-elect in the league, recording a thrilling 4-3 triumph over Pep Guardiola's side back in January.
"This club is already so full of history – we must now write our own history," Klopp told the media ahead of the mouth-watering tie.
"This team, we need to be proud of the club's history but also create our own.
"I've done that a lot in the past with my teams. [Borussia] Dortmund had a lot of history of course, but at some stage you need to do your own thing.
"The boys are ready – you could see it immediately after the last game."
Klopp confirmed Joel Matip, now ruled out for the rest of the season with a thigh injury, and Ragnar Klavan will not be available for the home fixture, meaning Dejan Lovren is likely to start next to Virgil van Dijk at the heart of Liverpool's defence.
Emre Can is also set to miss the first leg, the midfielder yet to fully recover from the back injury he sustained during the league win over Watford last month.
"He has a training session this afternoon, but even when we could need him really, we cannot rush it. That's how it is. There is no chance," Klopp revealed about Can.
"I'm always open to wait for better news but I don't expect it, to be 100 per cent honest. It could be not enough time [to face City], but maybe then Everton or Tuesday."
The German coach has a solid record against Guardiola, winning six of their 12 meetings, but insists past results will not be a factor in deciding the outcome of the tie.
"I never beat Pep – that was my teams [who beat him]. The record is not important. Pep is not worried about that record and I'm not proud of it," he added.
"Things like this are possible, that's why I love this game so much. If you can beat the best, that's enough on that day. We can beat the best, but only if we work hard and are smart."