Never during the two sides' fierce 122-year rivalry have Liverpool lost five successive matches against United, but they stand on the brink of the unwanted milestone after four straight defeats.
Liverpool boss Klopp has only been in charge for one of those games, having joined the club in October, and feels recent history will not affect the outcome of Thursday's last 16 first-leg match.
The squad at his disposal, he says, is much stronger than the one he had in January for the most recent victory in United's run, a 1-0 win at Anfield.
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"Manchester United have won the last four but it means nothing," Klopp told reporters on Wednesday.
"It would mean more if they had much more quality than us. But I think it is pretty close and we are both in a good moment...
"We are in a completely different situation (from the last game against United). We have more players available. We have to use this."
The most dominant run in the rivalry currently belongs to Liverpool, who won five successive matches between 2000 and 2002.
United's current stranglehold over the fixture, however, has been overseen by their coach Louis van Gaal, a long-standing rival of Klopp's, stretching back to when the pair were in charge of Bayern Munich and Borussia Dortmund.
Bayern coach Van Gaal won the first two of their four meetings in Germany, before Klopp won the next two, including a 3-1 win in Munich, Dortmund's first Bundesliga victory there in two decades.
Both managers have come through difficult periods in recent weeks, with Liverpool winning their last three Premier League games and United notching up four victories in a row in all competitions before Sunday's defeat by West Bromwich Albion.
"A few weeks ago there was a lot of pressure on Van Gaal, but they came through well. A lot of teams dream about their problems," Klopp said.
"I don't believe in enemies in football. I don't have a problem with Louis van Gaal but the last thing I want in this game is that he wins," the German added.
(Reporting by Toby Davis; editing by Ed Osmond)
