The Reds progressed to a fourth European quarter-final in five years – four of which have come in Europe’s elite competition – with a midweek win over RB Leipzig.
Such is their terrible Premier League form, taking 12 points out of the last 42, winning a seventh European Cup may be their best bet for qualification next season as they are well off the pace in the race for the top four.
But Klopp hopes to get his side, boosted by the win against the Bundesliga’s second-placed side, back on track at Wolves on Monday rather than pondering how to negotiate a way towards a third Champions League final in four years.
“It would be a dream eh? Why not? But we are not in a situation sitting here and telling the fairytale of how it could end,” he said.
“What we think, what we wish, what we dream of is completely different but being ready for Wolves is the only thing we’re busy with.
“Using the positives from the last game would be helpful. Yes, it’s the last eight but the last eight is historically tricky.
“I am not 100 percent clear who are the other seven or the few who look likely will be in but there are no easy games.
“In these games can we give them a proper game? Yes, definitely that’s the plan but not today, in three or four weeks.
“But we try to use it as good as possible.”
Liverpool’s chances of returning to form have been boosted by the restoration to midfield of Fabinho, who started his first game since October in his favoured position against Leipzig having deputised in central defence because of their injury crisis.
The Brazilian immediately not only brought balance to the side but brought the best out the team-mates around him.
“I’d like to start by saying Gini Wijnaldum did an incredible job,” added Klopp.
“When you play Gini at six you miss him on the eight as well, so a lot of things which were settled before were unsettled after that [move of Fabinho into defence].
“Yes, Fabinho helps everyone on the pitch in both directions if he can play his natural position.
“Yes, it makes life easier for Thiago as well but it’s not like we speak about it [saying] ‘one player back, now all the things will click again’.
“Unfortunately it is not like this but it helped that night because, for example, all three midfielders made a really good game.
“Fabinho played the first time for a long time at six and you could see the difference he can make in defending stuff but connecting as well, you saw Gini Wijnaldum on eight defending and always involved with his mind and Thiago as well, and that’s why it worked.
“When Fabinho can play the six it is obviously the best position for him and for us as well.”
Another positive from that night was Diogo Jota, who on Monday returns to the club he left in September looking for his first goal since November having just come back from almost three months out with a knee injury.
“It was a big miss. The moment he got injured, he was in a really good moment, which then makes it even worse,” said Klopp.
“What does he bring? It’s quality. He can play all three positions up front, he already played them for us, and on a really high level, which helps us. He makes us stronger, which is really good.
“It’s really important we have him back, for plenty of reasons.”