The holders return to the scene of last June's final victory over Tottenham on Tuesday as they face Atletico Madrid in the first leg of their last-16 tie at the Wanda Metropolitano.
The Reds are already well on course to win the Premier League title, as they lead the table by 25 points, and manager Klopp has his eye on further glory in this year's showpiece in Istanbul.
Due to their mammoth lead in the Premier League, it is fair to say Liverpool can now place more focus on the Champions League than they may have done had it been tight.
The way Klopp is speaking, that looks to be the case and another European Cup is in his thoughts.
"We don't feel like the winners of last year's tournament, we feel like contenders for this year's, and we want to show that," he said.
"We want to be there in Istanbul if possible, and for that we know we have to work our socks off."
Meanwhile, Klopp feels he has his work cut out against Atletico who, despite a difficult season in LaLiga, retain the toughness of their manager Diego Simeone.
Atletico are currently fourth after winning just one of their last five games but Klopp is full of admiration for Simeone, who has twice guided his side to the final.
"Yes, people will tell me that this year is not like it was, but it's a transition period. They are still fighting with all they have, you don't get many chances," Klopp added.
"If there's one team where you have to be at your absolute best, it's Atletico. They give you absolutely no presents. If you work as hard as possible, you have a chance. If you don't do that, you have no chance."