The Italian journalist claims Giovinco, 33, could quit Saudi club Al Hilal for Benevento in the coming months.
He adds that Gli Stregoni will offer Giovinco a deal up to 2023, when the player would be 36.
Benevento were 20 points clear at the top of Serie B when football was halted by the Coronavirus.
Giovinco would be a massive coup were he to agree terms with the Campania club.
The veteran left Juventus for Toronto FC in 2015, and took the MLS by storm with 83 goals in his four seasons there.
On 30 January 2019, Toronto sold Giovinco to Al Hilal for an undisclosed fee of between $2m and $3m.
The 23-cap Italy international has often been linked with a return home, and it may well be that Benevento is his destination.