An early start at Bournemouth on Saturday means Liverpool could overtake their rivals, who have an evening kick-off at fourth-placed Chelsea, but the German does not believe that will have much effect.
City have won 13 of their 15 matches -- Liverpool's best start to a season in their history has seen them win 12 games -- and already scored 15 more goals than their fellow unbeaten rivals.
"I don't think (Manchester City) feel pressure. They don't look like they do," said Klopp.
"That's not the first target anyway, the first target is to try to perform on the highest level, because it's needed at Bournemouth. Eddie (Howe) is doing a fantastic job there, and it will be difficult enough."
Klopp has to deal with a number of injuries with his team two games into a run of 10 matches in five weeks.
The loss of Joe Gomez for up to six weeks with a broken leg is significant, with fellow defender Dejan Lovren out with concussion and right-back Nathaniel Clyne still sidelined.
Klopp had been rotating youngsters Trent Alexander-Arnold and Gomez on the right side of defence, when Gomez was not partnering Virgil van Dijk in the centre.
The Reds boss admits he now has to come up with a plan to safeguard the long-term fitness of 20-year-old Alexander-Arnold.
It is likely to mean midfielders James Milner and Fabinho stepping in to give the young England international a break.
"It's just a shame for the boy," Klopp said of Gomez's injury. "For us he was in outstanding shape and he helped us a lot, especially because we could make these changes with Trent and Joe.
"That was really important because Trent is still a young boy and we cannot push him through 20 games in a row."
Klopp has other injury concerns, with Sadio Mane's cut foot meaning he is ruled out of the trip to the south coast.
He defended striker Daniel Sturridge after Burnley boss Sean Dyche accused the forward of diving to win a free-kick following Liverpool's 3-1 win at Turf Moor in midweek.
"Daniel Sturridge is no cheat," he said. "I think what Sean tried to do there is to bring up another subject so somebody could speak about that.
"It was a normal situation which can happen, sometimes a striker expects a tackle and tries to avoid it by jumping."