"I like Gattuso a lot and he will be the next coach of Palermo," Zamparini told Radio 2 in an interview.
The deal means Gattuso, who spent an unhappy spell as player-coach at Swiss club Sion this season, will move between two clubs renowned for unorthodox presidents.
The former midfielder, famous for his crunching tackles, was one of five Sion coaches to be fired this season by Christian Constantin who has employed around 30 managers since taking over for a second stint in 2002.
Palermo were relegated from Serie A this season after Zamparini used three different coaches, two of them twice.
At one point he fired Gian Piero Gasperini, replaced him with Alberto Malesani for three games and then brought back Gasperini before sacking him after two matches.
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