Rodgers, who was unable to bring a league title to the Anfield club, believes Slot can win over the fans.
The Dutchman is taking over from hugely popular, departing boss Jurgen Klopp.
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I think it is a transition," Celtic manager Rodgers told talkSPORT.
When someone has been at a club for so long like Jurgen, he has his stamp all over the club, the staff, the players. He and his staff will move on, one or two players will move on.
There will be that transitional period but Arne's a good guy. I came across him when we played Feyenoord in the Champions League this season.
His teams play good football and I am sure it will be a really good fit for him. Liverpool, another of those clubs, iconic club, big history, and I am sure he will go in and do really well."