Czech tactician Zeman left Pescara to take the vacant coaching position at Roma following Luis Enrique’s departure, and the promoted side are believed to be weighing up a number of options in the pre-season.
Gasperini, who is a free agent after his ill-fated spell as Internazionale boss, is keen on a quick return to the dugout and said he would speak to the Delfini.
"I will go and have a chat with the Pescara directors," Gasperini, 54, told Il Messaggero.
"I can’t really say anything else, apart from the fact that it would be a stimulating experience to boss a team like that.
"I’ll listen with interest to what they have to say, but I don’t know what will happen."
Despite his brief tenure at Inter earlier this season, Gasperini has an excellent reputation for his work at Genoa, who he led from Serie B to the Europa League in three years.
Pescara are also reported to be considering disgraced former Fiorentina boss Delio Rossi, ex-Cesena coach Marco Giampaolo and Italy U21 coach Ciro Ferrara, who managed Juventus during the 2009-10 season.