The Italy legend is interested in taking over the reins of the Rosanero following his sacking at FC Sion
The 35-year-old became the fifth boss to be sacked by Swiss outfit FC Sion this season when he was dismissed after just 12 weeks in charge earlier this month.
But the former Italy midfielder looks set for a swift return to the dug-out with the Rosanero, despite the fact current coach Giuseppe Sannino - one of three different Palermo bosses last term - remains in charge after the club were relegated to Serie B.
"I will meet with the president and evaluate," Gattuso told mediagol.it.
"In any case, I know that Palermo has a great heritage of enthusiasm, and that's why I'd like to come."
Zamparini then confirmed his interest in Gattuso and is confident the former midfielder will take charge of the club ahead of the new season, as soon as Sannino's "situation" is sorted.
"I really like Gattuso a lot,” he told Radio 2.
"He could be our new tactician just as soon as I have resolved the situation here with Sannino. I think Sannino has probably already resigned so we just have to reach an agreement."
Sannino began the season at the Palermo helm before being replaced by Gian Piero Gasperini. Alberto Malesani was then installed in February, only to be fired, with Gasperini returning once again.
However, his second spell lasted just two more games and Sannino was given the task of saving the club from relegation, something he was unable to do as they fell into Serie B for the first time since 2004.