The Giallarossi are reportedly ready to offer around £7.2 million, plus loaning Daniel Green, to secure the signing of the player from Serie A counterparts Sampdoria.
The news will come as a blow to the Saints, who were thought to be keen on a move for the forward who scored 12 goals in 30 games last season, with nine of those coming in the league.
It was believed he could be secured for as little as £5 million according to the Daily Star, although that now looks unlikely given the prices being quoted by La Gazzetta.
There is no denying that Ronald Koeman’s side need to add to their squad ahead of a Europa League campaign next season, with the forward positions currently one of their weakest.
While Graziano Pelle enjoyed a strong first season at St Mary’s, his back-up Shane Long is not known for being a regular goal scorer and the side suffered when Italian Pelle was missing for parts of the last campaign. That need may make them decide the extra cost is worth the effort.