The Reds have embarked on an impressive 15-game winning run in the top-flight that dates back to last season, to help establish them at the summit of English football once more.
They have however tasted loss twice this campaign, first at Wembley to champions Manchester City in their Community Shield clash, and subsequently against Napoli in their first European game of the new term.
Speaking ahead of his side’s visit of Sheffield United on Saturday, Klopp stated that he wants his side to remain sternly focused on matters on the pitch, and not to be get carried away by their record-breaking sequence of results.
“We don’t think about it, only when I am in a press conference! It’s just the next game,” the German revealed as he prepares for the trip to Bramall Lane.
“Thank God we lost from time to time in the Champions League or other cup competitions, because we still know how it feels. That’s really important because we want to change things when we lose a game.
“We just want to go to Sheffield and make their life as uncomfortable as possible. That’s the plan. We are considered as a top team but we don’t want to behave like a top team. We want to fight like a proper challenger.
“I don’t see any reason why there should be an advantage for Sheffield besides the fact they are playing in their own stadium.
“Is it allowed that they fight more than us? No. Is it allowed that they run more than us? No. Is it allowed that they just do more than us? No.
“We must be there, absolutely spot on. That’s the plan. We planned the week so the boys will be ready. Now we go there and we are really looking forward to it.”
Klopp has seen his team open up a five-point gap over City in second, but he is likely to resist the temptation to give more game time to a string of youngsters who impressed midweek in the Carabao Cup against Milton Keynes Dons.
Defender Ki-Jane Hoever was on the scoresheet while 16-year-old midfielder Harvey Elliott was another to impress in a 2-0 victory.
“I think they are ready. But you need to find the right moment. They have to learn and develop a lot,” Klopp added.
“It was really nice [at MK] I think for Harvey it was the most obvious with the things he did on the pitch. We are not in doubt about these boys, and we know what we want to do with them and what we expect from them. But the best news is that they have all the time in the world.
“They are part of a really strong squad and it is not easy to come into a team like this. But they are as close as they have to be. We work hard with them so they can make the next steps.
“They have to be patient, but you see when you let them off the leash, they are obviously ready for some really nice football things.
“There’s a long way to go but we don’t prepare them for one Premier League game, we prepare them for a Premier League career, in the best way we see. That’s what we want.”