The Reds won the Champions League last term and have already lifted the UEFA Super Cup and FIFA Club World Cup in 2019/20.
Klopp’s side are 13 points clear at the top of the Premier League table and among the favourites to win the Champions League for a second season in a row.
And the German insists he is still hungry to win as much silverware as possible at Anfield.
“Is it greed? I’m not sure,” he told ESPN. “It’s like this desire you want to have trophies. I don’t think it’s real greed.
“We have improved our opportunities obviously with different things, with the players we brought in and to work together for a while of course with more experience. Stuff like this.
“Getting used to different situations more and more [is helpful too]. You know a defeat is a defeat, but if you learn, it still makes sense, like the Champions League final [defeat byReal Madrid] the year before, when [Liverpool] lost that.
“It’s not that we really learned something from the final, but the way to the final or the way to the next final, the experience for me before helped us a lot.
“I really think our desire is immense. It’s big, it’s massive to win more trophies. If it’s greed, I don’t know, but yeah. Who cares?”
However, Klopp believes it will be extremely difficult for Liverpool to win each of the three competitions they remain in – the Premier League, the Champions League and the FA Cup.
“A lot of teams can do that to be honest. OK, with the Premier League, maybe it’s now three teams. I don’t know exactly who can win it still, and the Champions League there are still 16 teams who can win it.
“The FA Cup? I don’t know exactly how many teams are in still, but that’s how it is yes. The good thing is that if you think about it, you don’t think we have no chance, and that’s a start. We have a chance. But we knew that.
“I remember two years ago, before when we qualified for the Champions League after the Hoffenheim game, we had a meeting. I said to the boys, ‘look, in the competition there are maybe 10 clubs who can win the Champions League.’
“There were more teams in obviously at that moment, a lot of teams are part of it, but about 10 clubs can win it. We are one of them. It doesn’t feel in the moment like this, but we are. That’s what we should try, and that’s how we took the Champions League, for example.
“With the Premier League, it’s slightly different and difficult when you see the dominance ofMan Cityfor the past three years. You work on that, you hope for it but you don’t know exactly.
“So we are no dreamers. We are just quite positive about our skills and our relationship and the things we do together and the things we want to achieve together.
“So we will see what happens. Nobody knows if we win one of these trophies, but we will work of course.”
Liverpool are next in action on Thursday, whenSheffield Unitedmake the trip to Anfield.