The next step of their quest comes on Tuesday with a trip to Atletico Madrid in the first leg of their last-16 tie.
Asked to assess their chances of emerging victorious in Istanbul in May, Klopp struck a cautious note.
Speaking ahead of Saturday's league clash with Norwich City, he told reporters: "Juventus were my favorites before the season started but obviously I don't watch Italian football enough because I cannot work out why they are not 10 points ahead at the top of Serie A.
"They have the biggest squad I have ever seen in my life; quality players too, it's crazy.
"The Bayern Munich squad is also massive, PSG are incredible when they are all fit, you can never discount Barcelona and let's not forget Manchester City because the Champions League will be one of their big targets.
"I have no clue how far we can go but there's no need to think about it yet because at the moment all we need to concentrate on is Atletico on Tuesday."
The German has built a formidable squad on Merseyside but believes the level of quality elsewhere in Europe means it will come down to a few crucial moments.
He added: "I have no clue if we can win the Champions League again, but we should be ready to go for it.
"What I know and what we showed last year is that we can beat the best. It doesn't mean we will, it just means we can, and that is the only thing I have to know.
"There are so many strong teams out there you have to be ready for the fight, then it's about luck in certain moments to win anything.
"In the end the quality within a squad is not always the biggest difference, it's more about who can find the right mood, show the most desire, be decisive in the right moment.
"And luck. To win anything you will need that for sure."