"There hasn't be an official announcement yet -- but I don't think it will come as news to you that I will be coach there next season," Slot told reporters.
The BBC said last month that Slot's deal to replace Klopp was worth up to £9.4 million (10.9 million euros).
"The feeling that I'm leaving here is getting stronger. There are some people you don't simply just want to shake hands with," Slot said ahead of his last game at the club.
"At those times, it's not about whether you have become a champion or won the cup, but more about the appreciation between people," he added.
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 before penning a new three-year deal.
"You can see people are genuinely sorry you are leaving," he said.
"You can say that with words, but when you see it in people's faces, it affects me quite a lot."
The Feyenoord club website said a farewell party was being organised at the raucous De Kuip stadium after Slot's final game, against Excelsior.
'Great job, great team'
Feyenoord have enjoyed a strong season, winning the Dutch Cup and coming second to an all-conquering PSV Eindhoven side with one game remaining.
But Slot has only lost two league games all season and noted: "If we win (on Sunday), we will have 84 points and we will be the second best Feyenoord team in club history."
Under Slot, Feyenoord have delighted the fans in De Kuip with an attacking brand of football and the 45-year-old won praise from Klopp himself.
"I like the way his team plays football. If he is the one, I like that he wants it," Klopp told reporters last month.
"It's the best job in the world, best club in the world. Great job, great team, fantastic people. A really interesting job," said Klopp.
Liverpool captain and fellow Dutchman Virgil van Dijk has also hailed Slot's attacking mindset, saying it would suit the philosophy at Anfield.
"I think the way of playing and the philosophy he has, that he could be a Liverpool coach," said Van Dijk.
A fan of Manchester City manager Pep Guardiola, Slot was a slick forward as a player with a reputation as an accurate passer of the ball -- so much so he has a move named after him.
The Arne Slot Pass is a slight deflection from a forward with his back to goal which splits the defence and releases a winger running off the ball.
Klopp will step down as Liverpool manager at the end of this season after a nine-year reign which brought the Champions League title in 2019 and Premier League trophy a year later.
Initially, Bayer Leverkusen boss and former Liverpool midfielder Xabi Alonso had been the favourite to succeed Klopp.
However, Alonso has committed to staying at Leverkusen after leading them to a first-ever Bundesliga title.
