The Toffees have turned to the Italian after Arsenal hijacked their move for Deportivo La Coruna forward Lucas Perez.
Everton scouts have watched Gabbiadini over the past six months and they have returned with positive reports.
And now, according to Radio Kiss Kiss, the Premier League club are closing in on a swoop for the 24-year-old worth £20m.
Gabbiadini has provisionally agreed personal terms with Ronald Koeman’s side and they are currently negotiating the payment structure of his transfer fee.
The Serie A club are also eager to bring in a replacement for the Italian before he leaves, with a move for Fiorentina’s Nikola Kalinic on the cards.