The coach has to speak Italian. Whether he is put in place 6-12 months before or they have a crash course over pre-season, whatever, they can come from Zanzibar or wherever, but they have to have a grasp of Italian early in the season.
Doesn't at all mean they have to be Italian or Serie A-experienced, but there is an inevitable learning curve for anyone coming into the league. That's the same for most leagues.