Gasperini will bring new ideas to the club after replacing Leonardo on the bench, but Zanetti is optimistic about future success.
"In these years we have won trophies and done well," he told the Corriere dello Sport. "Even last season, despite the difficulties, we lifted silverware.
"We want to do the same with Gasperini, starting with the Italian Super Cup. Then we'll fight for the Scudetto.
"I've spoken to the new Coach and he made an excellent impression on me. He loves to work and his Genoa side played excellent football."