The Dutchman is said to be very keen on replacing the well-liked German, following initial talks, and both clubs are believed to already be in negotiations.
Slot is a bit of an unknown to fans of Premier League clubs who, apart from the Champions League, watch little club football on the continent.
Perhaps the British would best know the 45-year-old as the man who led Feyenoord to the 2022 Europa Conference League final, but he has enjoyed more success in the Netherlands.
Slot delivered Feyenoord their 16th Eredivisie title in the 2022/23 season - their first since 2016/17 - and won the Dutch Cup earlier this term.
And that's all well and good - but what makes him the man who could replace Klopp at Liverpool?
Well, I don't know. But I know someone who does. Paul Winters, one of Flashscore's editors in the Netherlands, took a few of my questions.
SC: Is Slot's style translatable to the speed of Premier League football?
PW: "Slot's style involves a high press, creative freedom and a lot of influence from the full-backs, who work in similar ways to how (Trent) Alexander-Arnold likes to play at Liverpool.
"Slot's Feyenoord (are) known for having an insane motor. They keep going for the full 90 minutes and never let anything get down to luck. The high press is almost reminiscent of Klopp's blitzing style of play, so I think Slot's perspective on football will translate well to England - and especially Liverpool."
After almost a decade of Klopp, Liverpool fans have got used to quite a lot about him. Is there anything about Slot they should be prepared for? Personality quirks and so on...
"If you like Klopp, you'll like Slot. He's passionate, but friendly. He's serious, but playful. He's insightful, but jolly. He's got the full package when you listen to him, and his calm way of addressing the media. He breathes football, was a bit of a stylish player himself before he retired in 2013, and knows what's going on in the heads of his players.
"Players adore him, I've never heard of a player falling out with him. That makes me think he will be capable of managing a top team, although he might need time to adjust to this experience and demographic.
"Under the limelight, everything is different. But he's (already) been to the higher stages of European football with a (Europa Conference League) final and a (Europa League quarter-final) outing in 2022."
How do you think he'd cope with the English media? I mean, the bizarre TV slots and kick-off times that have irked Klopp and Pep Guardiola...
"The shift to English football will be something for Slot, but he's enough of a football maniac to enjoy that aspect of it. I'm not sure if it'd get to him, but if anything (does) I believe he'll manage."
It feels like low-hanging fruit, but where does he differ from Erik ten Hag? Why is he better-equipped to make a success of a move to a big Premier League club?
"Slot and Erik ten Hag differ in terms of playing style. Ten Hag had his squad completely tailored to his style of play and even used different tactics in Europe with playing (Dusan) Tadic as a false-nine instead of a left winger.
"Slot plays more of a rock-'n'-roll style of football, more on the nose; he relies on the engines of his squad, of their creative abilities, and makes them work accordingly to where their strengths lie.
"I'm a fan of Ten Hag after his time here, but I feel as though Slot would have Liverpool play less of a self-imploding, volatile style of football, unlike Ten Hag at Manchester United."
Why has it gone so wrong for Ten Hag at Man Utd, when he was so highly-rated at Ajax?
"Erik ten Hag was dominant in Dutch football and had a specific style of play at Ajax that he almost perfected with the players he had. He had his pawns everywhere on the field, everyone had a specific task and kept themselves to it. (Hakim) Ziyech had a free role, Tadic was the epicentre of the attack, (Noussair) Mazraoui was the inverted full-back, (Nicolas) Tagliafico ran back and forth along the left side, (Donny) van de Beek was the raumdeuter and players like (Matthijs) de Ligt and (Frenkie) de Jong were instrumental in the build-up from the pivot.
"The fact he was able to build this at Ajax is because, even though it's a big club, it's not Manchester United. At United, and in the Premier League in general, your every movement is monitored. Every game feels like another final and if you slip up, you'll hear it. There's a smaller room for error and Ten Hag hasn't been able to emulate the type of play from Ajax to United."
Back to Liverpool, which player do you think would struggle most under Slot?
"Slot loves his six, his hard-working central defensive midfielder. It's a role slightly missed at Liverpool. At Feyenoord, he has Mats Wieffer, who they bought from Excelsior in 2022, and has since grown to be a stalwart and a Dutch international. He works tirelessly, has excellent defence in his arsenal and could be seen as one of the few lesser creative players in Slot's side.
"I don't see an equivalent of Wieffer walking around at Liverpool, so someone from the midfield will have to either adjust to this role or relinquish their spot to a more suitable type of player. I can't pinpoint one specific player who might struggle under Slot, but all of his players will have to get in their seventh gears from time to time to show him the work ethic he desires."
Would Slot be likely to bring over any of his Feyenoord stars? Or anyone from the Eredivisie? Who would be best-suited for a move like Liverpool?
"Looking at the Eredivisie, there are only a few candidates I could see Slot take with him to Merseyside. David Hancko has been absolutely excellent and has made Marcos Senesi almost become forgotten in Rotterdam.
"An obvious shout is Santiago Gimenez, who's been an excellent striker under Slot. Left-back Quillindschy Hartman would've been a suitor too, but he just suffered a serious knee injury and will stay at Feyenoord this coming season.
"Perhaps Slot would love to take Wieffer with him. Looking further, you'd have to give PSV's Johan Bakayoko a look after this extremely dominant season from the Eindhoven outfit."
Do you think he'd struggle to adapt to life in the UK? We don't really sell bitterballen here!
"I think Slot will be just fine in England. He's passionate about the game and a genuinely likable and easy-going man. I don't foresee him running into trouble without easy access to bitterballen or stroopwafels (laughs). At least he'll have the rubbish weather he's used to!"
