Having just been named coach of Heerenveen, Van Persie worked with Slot at Feyenoord.
The former Manchester United and Arsenal striker told ESPN: "I think (he'll do) very well, very well.
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"How he wants to play is in line with (Jurgen) Klopp's style of play and what they are used to there. I expect them to do very well. Liverpool is one of the nicer clubs in England. I have been able to play for two other very nice clubs.
"Slot has already been able to practice well at Feyenoord in that rhythm, but there (England) it goes very hard and fast for 11 to 11.5 months a year. It is a very nice, new opportunity for him. I believe it will go very well."