Slot led Feyenoord to their first league title in six years but has been heavily linked with a move away from the Dutch champions in the summer.
He has been gradually emerging as Tottenham’s top target in their pursuit of a new manager ahead of next season.
There are suggestions that Tottenham are looking to hold talks with Slot soon but Arnesen, who brought the Dutchman to Feyenoord, stressed that he needs to be careful when choosing his next club.
He insisted that the Feyenoord boss will have to find the kind of club that will allow him to work the same way he has been at the Rotterdam club.
Arnesen also stressed the importance of getting the timing right to leave Feyenoord and finding the right club.
The former Feyenoord technical director said to Dutch magazine Voetbal International: “Arne is only 44, don’t forget that.
“If he leaves, his choice has to be good, in the sense that he can work as he does at Feyenoord.
“You then talk about the right club, right offer and at the right time.”
Slot is reportedly likely to demand complete control over first-team affairs before accepting an offer from Tottenham.