The 27-year-old made his international debut in the Azzurri's 3-0 win over Northern Ireland in a friendly exhibition on Saturday.
Former Roma man D'Agostino made no secret of his desire to join a high-profile team, after spending the last few years at Italian minnows.
"I said I wanted a big club and Juve are among the biggest," he said. "When (Ciro) Ferrara left the other day, he winked at me as he went out the door."
Ferrara has been appointed as the Old Lady's boss a couple of days ago, and stepped down from his role as an assistant of Italy head coach Marcelo Lippi.
Udinese are yet to agree a deal for D'Agostino, who has been valued at £28 million.
According to Italian reports, club president Giampaolo Pozzo is seeking to land two players from Turin in return for D'Agostino.
Sebastian Giovinco, Claudio Marchisio and Paolo De Ceglie are believed to be the purposed names for a part-exchange deal.