The 21-year-old centre-half is among a group of promising Australian starlets currently being linked with moves away from their homeland.
Sainsbury has starred for the Mariners this season and is being tipped to make his senior international debut in the not too distant future.
Southampton are said to have been impressed by scouting reports they have received on the highly-rated defender.
FC Basel and Roda JC Kerkrade are also keen, having offered trials to Sainsbury, and his current club concede that they face a fight to keep their squad intact for the Asian Champions League.
Mariners coach Graham Arnold said of Sainsbury and fellow youngsters Mat Ryan and Bernie Ibini: "There has been a lot of interest in all three parties so I know there's always the chance of something happening.
"We will have to wait and see."