The Sky Sports report says at least one of those clubs have already submitted an offer for the player, as confirmed by Saints manager Ralph Hasenhuttl.
Gabbiadini has only made one appearance for Southampton under Hasenhuttl since the manager was hired in December - a late substitute cameo against Cardiff City.
After the game, Hasenhuttl said the club have received offers for Gabbiadini.
”Sure [they have had bids], we have to decide and he has to decide where he wants to go,” Hassenhuttl said.
”There are a few teams interested in Manolo, we will have a look and if there’s a result, we’ll tell you.”