The Serie A side have allegedly secured the services of the promising Argentine, who has been linked with a move to a top European club in recent months
The 18-year-old forward has been strongly linked with a move to Europe after establishing himself as one of the hottest prospects in South America.
A host of European giants have been associated with Dybala, but Zamparini claims that Palermo have beaten all competition for the Argentine's signature.
"We have secured Paulo Dybala," Zamparini told Sky Sport Italia. "He is the new Sergio Aguero.
"Inter, Paris Saint-Germain and Chelsea also wanted him."
Dybala has scored 17 goals in 30 appearances for Instituto, who sit at the top of Argentina's second tier, one point ahead of River Plate.