In fact, two of their trips to Goodison Park have ended in complete disarray, offering a stark warning ahead of this weekend's clash.
Arne Slot's side make the short trip over to enemy territory with an impressive Premier League lead after a record start from the Dutchman.
However, nine points clear was reduced to seven last time out thanks to a 3-3 draw with Newcastle, and the Reds will be wary about what can go wrong at Goodison.
Overall against the Toffees, Klopp had a record of 11 wins, six draws and two defeats in 19 games, yet despite all those points, some of the tougher matches were incredibly damaging.
At Goodison, which is about to host its last every Merseyside derby before Everton move to the 52,000 Bramley-Moore Dock Stadium, Liverpool's record has been far less favourable with two wins, five draws and a defeat, and it was one of those draws that left some damage that was long feared to be irreparable.
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On October 17, 2020, reigning champions Liverpool headed to their rival's empty stadium for a match behind closed doors during the Covid pandemic, and Jordan Pickford ended the match thankful that there wasn't an away end to abuse him.
Everton entered the game top of the league under Carlo Ancelotti, but went behind to a Sadio Mane goal just three minutes into the match.
Eight minutes later, catastrophe struck for Liverpool when Pickford flew out of his goal to challenge Virgil van Dijk at a corner, and clumsily made contact, pushing the defender's knee into a painfully unnatural position.
The defender was able to leave the pitch of his own accord, but as it turned out, the incident had torn his anterior cruciate ligament, and he wouldn't play again that season.
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Van Dijk then missed his first major tournament with the Netherlands that summer, and upon his return there were fears he'd never get back to his Ballon d'Or challenging level, although some would argue he's now at his best once again.
However, in the short term it was bad news for Liverpool. The match also saw Richarlison sent off for a horror challenge on Thiago, and what looked like a late Jordan Henderson match-winner was ruled out for offside.
The game would end 2-2, and it began a season of endless injuries for the Reds who somehow still salvaged fourth place and Champions League football, but their title bid was well and truly over.
Speaking post-match, Jurgen Klopp said: "What can I say? I can't find the words… I don't want to say Jordan Pickford wanted to do it… but it is of course not a challenge a goalie can do in the box because there is another player there."
That match has also taken a turn in recent weeks given that David Coote was in charge of VAR on the day, with Liverpool fans citing his decision not to advise a red card for Pickford amid his comments about the club and then-manager Klopp.
It was understood that Pickford avoided a sending off as the play was offside, something on-pitch referee Michael Oliver later addressed, saying: "We have all, myself included, not thought about the challenge as much as we should have done. We could still have given offside and sent Pickford off."
The 2020/21 campaign really would go on to become one from hell for Liverpool, but they would regather for a quadruple charge the following season, and then do the same against last time out in 2023/24.
Yet it was once again at Goodison where everything went wrong.
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Liverpool started the campaign at an extraordinary pace on all fronts, and took home the Carabao Cup in February to show they were serious.
Out of the Champions League, it looked like the Europa League would be a cakewalk for them, yet things began to crumble in March in dramatic fashion.
First exiting the FA Cup at the quarter-final stage against Manchester United, April then saw another shock as Atalanta dumped them out of Europe also in the final eight.
With just the Premier League left to challenge for in Klopp's final season, they headed to Goodison with five games left to play level on points at the top of the table with Arsenal.
For Everton, it was a chance to end their season on a high, and they did so by finally getting their first home win against Klopp with a shock 2-0 scoreline.
Goals from Jarrad Branthwaite and Dominic Calvert-Lewin took the three points on the day, and sent Liverpool packing.
Two more draws followed in their final four games, enough to rule them out of the title race and leave Klopp apologising.
"We were not good enough, we have to admit it," the German said post-match. "I really apologise for that.
"We need a crisis at Manchester City and Arsenal and we need to win football games because if they start losing games and we do what we did tonight, nothing changes."
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That crisis never came, and Klopp left Merseyside with his final derby experience one to forget, and perhaps a warning for Slot as he gets set for his first.