On Tuesday night, Gabbiadini scored the only goal of the game as Southampton defeated relegation rivals Swansea City, and the strike could prove enough to keep the Saints in the Premier League.
However, Gabbiadini has only played a bit-part role for the south coast club this season, and according to Calciomercato.com, it has resulted in the player wanting to sign for a club back in his homeland.
The 26-year-old allegedly wants to be regarded as first-choice forward at a team playing in Serie A, and a number of teams are said to hold an interest.
Gabbiadini still has over three years remaining on his contract, but the Saints are unlikely to stand in the former Napoli man's way should he wish to leave the club.
The player has scored five goals in 11 starts and 17 substitute outings in the Premier League during the current campaign.