Southampton should try to secure a deal for the Brazilian by offloading a striker who has found opportunities hard to come by.
Southampton have been credited with an interest in Lazio winger Felipe Anderson, but face strong competition from West Ham United in order to sign him this summer according to the Guardian.
The player's agent has told Tuttomercatoweb that his client is actually happy at St. Mary's Stadium, but that is difficult to believe given the amount of game time he got last season with the quality he possesses.
Gabbiadini made 28 Premier League appearances last time out, but only 11 of those were starts as he struggled to dislodge Shane Long and Charlie Austin from Southampton's starting XI and gain the trust of Mauricio Pellegrino and then Mark Hughes.
Southampton have been linked with a move for Anderson, and they could kill two birds with one stone by offering cash plus Gabbiadini.
The Italian has excellent predatory instincts in the box, as demonstrated in the early stages of his Southampton career, and could make for a nice signing for Lazio - especially with Ciro Immobile's stock pretty high at the moment.