Pep Guardiola’s side are 10 points clear at the top of the table, having won 12 successive league matches, and the 16-point gap to last season’s champions has already seen Klopp concede the title.
But the Reds boss insists what City are doing this season is not the driving force behind his own plans for improvement.
“We do not have to think about that now because we do not play them any more this year, probably. Maybe in the Champions League,” he said.
“It was never the case where we thought ‘how can we overtake City?’, or ‘how can we become the finest team in English football again?’.
“We just wanted to be the best version of ourselves. We have that chance again. If that is good enough, it is good enough. If another team is better, that’s how sport works.
“We cannot do more than be the best version of ourselves and that is what we will try again as a team. For that we need a little bit more luck, of course. Slightly more luck with injuries and we can get closer to that.”
Klopp has lost all three of his senior central defenders to injury, with first-choice pair Virgil Van Dijk and Joe Gomez both suffering long-term problems within a couple of weeks of each other two months into the campaign.
Summer signing Thiago Alcantara also missed 16 matches with an injury sustained in October, barely a month after arriving.
“We all agree, and I’m sure Pep would say that, in a normal season for both teams we would not be 16 points away. But we are. That’s how it is. We accept it,” added Klopp.
“This season it is not our concern how close we get to City. It is how far we can go up the table. That is enough work to do.”
Having slipped to sixth place after just two wins in their last 10 league matches, the visit of Everton – three points behind with a game in hand – for the 238th Merseyside derby is a crucial one.
The Reds have not lost at home to their neighbours since September 1999 but their formidable home form has deserted them having gone five matches without a win.
October’s derby at Goodison saw Thiago sidelined for two-and-a-half months and Van Dijk’s season prematurely ended due to a reckless Jordan Pickford tackle.
And while Klopp said there would be no payback from his players, he does want them to be “emotional”.
“We always are emotional. That is our way to play. What the other team does, I have no influence. Nothing to say about that,” he said ahead of the third derby played without fans because of coronavirus restrictions but the first held at Anfield.
“I can imagine after the first game [the media] try to create some stories around that, but I – we – are prepared for a football game, a derby, like we always did.
“Nobody can ever say this team was not ready for derbies from an attitude point of view, or from an understanding point of view.”
Klopp, whose own record of 12 derbies unbeaten is a club record, beating Bob Paisley’s 10, added: “Of course, the derby is a derby without supporters, but with supporters it is just much more enjoyable.
“We all love when football becomes the most important thing for a few moments. This intensity I really like. The game is still intense, that’s normal.”