The Reds finished fourth last term, but their run to the final of the Champions League and subsequent summer business has led to many installing them as second-favourites to lift the trophy this time around, behind only the defending champions.
Liverpool got their campaign off to an encouraging start with a 4-0 triumph over West Ham United which leaves them top of the table after the first round of matches, but Klopp insists that he has paid little heed to suggestions that his side could end their 28-year top-flight drought.
"I couldn't be less interested in what other people say of us. We said it before the game again, what people say is sometimes nice, sometimes not so nice, but it is always not important," he told Sky Sports News.
"What is important is that we know what we want to be, and we want to be a challenger. How can we be something different? We didn't win anything in the last few years, that's the truth. And the other teams, I can't see that they've got weaker. So why should we [be the only challengers] because we made a few signings?
"It's only an English thing, where you can win the league in the transfer window. It's not possible. It's not interesting. We did our business, other teams did theirs last year, two years ago, whatever. We did it this year because we felt it was the right moment to do so, that's all! We enjoy our role, and all the rest is not important to us."
Liverpool's second match of the campaign sees them take on Crystal Palace next Monday night.