And it could be one that benefits former Manchester United manager Erik ten Hag.
Klopp officially joins the RB project on January 1 and will already have one tough task on his hands with ex-Liverpool assistant Pep Lijnders massively struggling at Red Bull Salzburg with a five-game winless run in the Austrian Bundesliga.
And things aren't any better at Red Bull's other headline act - Leipzig.
The two-time DFB Pokal winners looked like Bundesliga title contenders to start the season, but now with three losses in four they're completely out of the picture.
On top of that, they're 34th in the Champions League league phase with five defeats from five games.
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That's led to strong talk that head coach Marco Rose could be fired, and according to Dutch football expert, Marcel van der Kraan, Ten Hag could be Klopp's pick as a replacement.
"He was linked with RB Leipzig before joining Man United - and they are having a right struggle," he told talkSPORT.
"They lost all their games in the Champions League, they got a hammering of 5-1 [against Wolfsburg] their coach Marco Rose is under big pressure.
"I think they are looking at him [Ten Hag] at the moment, and it could be a moment where Man United think, 'Ooh maybe that will save us a few pennies if he joins them soon'."
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Making way for Ten Hag would certainly be heart-breaking for Klopp, though, with Rose his first true prodigy in football coaching.
Rose played over 150 games for Klopp at his first club Mainz and the two adored each other, with Klopp later saying: "I trust Marco in everything.
"Marco could do any job and do it well, he is really the most hyped coach at the moment, everyone is asking about him."
Despite their incredibly close relationship, Klopp may have a tough decision to make, and Ten Hag could well be a fitting replacement.
The Dutchman previously worked in Germany where he impressed with Bayern Munich II under Pep Guardiola's first team.
He then went to Ajax and led a young homegrown squad to within a whisker of the 2019 Champions League final, later joining United in 2022.
Ten Hag's rollercoaster term Old Trafford came to an end after a loss to West Ham United in October and has since been replaced by Ruben Amorim.
Despite a potentially frosty reunion with Klopp on the cards, Ten Hag's new job could be good news for Man United.
Ten Hag and his coaching staff have already been paid £10.4million in compensation after the Dutchman was sacked.
United then paid Sporting around £11million to bring Amorim, along with six members of his team.
These figures have been taken from the club's first quarter results and mean the total sum sits at approximately £21m.
Ten Hag's contract at Old Trafford ran until 2026 - and Dutch football expert Van der Kraan suggests United could escape paying further compensation if their former boss lands a new job soon.
If the Dutchman does join RB Leipzig, he will be hoping for a more generative tenure than at his time at Old Trafford.
At the time of his dismissal, the Red Devils had won just four games out of 14 and sat 14th in the Premier League.
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They also failed to win any of their three games in Europe and were 21st in the Europa League table out of 36 teams.
Speculation that Ten Hag would be sacked at the end of the 2023-24 campaign circulated but after United beat Manchester City to lift the FA Cup, they kept him in place for the current season.
United minority owner Sir Jim Ratcliffe considered sacking Ten Hag in the summer and the club held talks with various replacements.
But the club eventually opted to trigger a contract extension until 2026 after carrying out an extensive review and introducing a new sporting structure, with Dan Ashworth appointed sporting director, Omar Berrada as chief executive and Jason Wilcox as technical director.
United chiefs wanted to give Ten Hag time to work within the structure and following £200m investment in new players.
That summer took the total expenditure on players under Ten Hag to beyond a staggering £600m.
But there was little upturn in form this season and Ten Hag ran out of lives when Man United lost to West Ham, preceded by a draw to Jose Mourinho's Fenerbahce in the Europa League.
His potential new destination, RB Leipzig, currently sit fourth in the Bundesliga table, nine points adrift of leaders Bayern Munich.
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The Red Bulls are also yet to earn a point in the Champions League and they have not won a match in over a month.
With a shaky season already ongoing at the Red Bull Arena, it will be interesting to see if Klopp decides to bring in his old foe.