Feyenoord boss Slot leading race for Liverpool job - reports
Slot, 45, led Feyenoord to their first league title in six years last season and won the Dutch Cup on Sunday.
He had been a front runner to take over at Tottenham a year ago before ruling himself out of contention.
Sky Sports, the BBC and The Times all reported that Slot is now leading the race for the unenviable task of following Klopp at Anfield.
However, the Reds could face competition from Bayern Munich and Barcelona, who are also looking for new coaches next season.
Bayer Leverkusen boss and former Liverpool midfielder Xabi Alonso had been the favourite when Klopp announced his decision in January to stand down at the end of the season after nearly nine years in the role.
However, Alonso has committed to staying at Leverkusen after leading them to a first-ever Bundesliga title.
Sporting Lisbon coach Ruben Amorim was also linked with the Liverpool vacancy but reportedly held talks with West Ham on Monday about replacing David Moyes next season.
Slot moved to Feyenoord in 2021 after impressing in his first managerial role at AZ Alkmaar.
He led the Dutch giants to the inaugural Europa Conference League final at the end of his first season, in which they narrowly lost 1-0 to Jose Mourinho's Roma.
Slot then delivered just a second league title in 24 years to De Kuip last season, but his side trail PSV Eindhoven by nine points with only four games remaining in this year's Eredivisie title race.
The Times said his track record of improving players and a high-octane playing style, not dissimilar to Klopp's, is what is attracting the Liverpool hierarchy.
Klopp has just five games left of a reign that has transformed Liverpool's fortunes after decades in the doldrums and could yet go out on the high by winning the Premier League.
Liverpool sit behind Arsenal only on goal difference at the top of the table, but Manchester City have the destiny of the title in their own hands as they are just one point behind the top two with a game in hand.