The 23-year-old Italian missed out on the GP2 title to Pierre Gasly in 2016, but is unlikely to stay in the feeder category for another season.
Now La Gazzetta dello Sport is predicting that Giovinazzi will take the third driver role at Ferrari for 2017.
"In the coming days, perhaps at the Christmas lunch with journalists at Maranello on Monday, Ferrari is expected to announce Giovinazzi's arrival in the (development) Academy," the Italian report said.
La Gazzetta said that his manager Enrico Zanarini was key to the deal, thanks to his experience handling the careers of former Ferrari drivers Eddie Irvine and Giancarlo Fisichella.
Giovinazzi had previously been linked with a move to Mercedes as part of their young driver scheme. He was allegedly offered a DTM seat for 2017 but he turned down the German marque's offer.
He also conducted simulator work for Ferrari during the 2016 season.
Bahrain International Circuit - Winter testing