Bolton are understood to have offered the 21-year-old Perth-born defender a trial in the summer, while Dutch club Roda JC have also invited him to Holland for a similar arrangement.
Southampton have been monitoring the form of Sainsbury all season and have been impressed as he has helped his club - the Central Coast Mariners - reach the A-League Grand Final.
Reports in Australia suggest Mariners coach Graham Arnold is ready to let him go to try his luck in Europe - but that he will stay with Central Coast until after their Asian Champions League group stage matches end on April 30.
A £500,000 fee could be enough to secure his signature with Southampton still near the front of the queue for his signature.
The defender was included in Australia's squad for the 2011 U20 World Cup in Colombia and is tipped to make the full side in the near future.