In the press conference about the game against Arsenal this Saturday, the German coach didn't want to hear about a Premier League in which only two teams opt for the title.
"The most important thing for me is not that it is a fight between two teams. Even if it were, we don't know if we would be the second team. We have a lot to prove yet," Klopp explained.
Last year, Liverpool finished second, just behind Manchester City, and with Chelsea in third place, in one of the most equal battles between two teams in recent times.
"The last was the first time that we had a season like this, so how are we going to take it for granted that it will happen again? There is still room for improvement," added the German.
Liverpool and Arsenal come up against each other this Saturday (16:30 GMT) as the only teams who have achieved two victories in their two opening games and as leaders of the Premier League.