The Dutch coach, who is in charge at Feyenoord at present, is seen as a huge coup for the Reds.
Slot was targeted by Tottenham last summer, but they preferred Ange Postecoglou.
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Dutch World Cup legend Johnny Rep told The Sun: Arne has what it takes to fill Klopp's big boots and it's possible he'll win the Premier League in his first year.
Arne has done great things at Feyenoord, winning both the league and the cup, and I can't wait to see him do the same in Liverpool.
He has all the credentials to manage a club as big as Liverpool because he's simply an excellent coach."