The Queens Park Rangers striker has long been linked with a move away from Loftus Road and his contract with the west London club expires at the end of the current season.
He has pledged his immediate future to QPR and is 4/6 to remain with the R's beyond the current transfer window.
But Southampton have shot up to 5/4 to bring the 26-year-old to St Mary's - a move that would make a lot of sense.
Southampton need goals and have seen their strikers suffer in front of goal so far this season. The Saints are 12th and in no immediate danger of being dragged into a relegation battle - but their form has suffered over the last few weeks. A surefire way of improving that would be to bring goals to the South Coast.
While several previously linked clubs now seem to have gone quiet in terms of the Austin market, Sky Bet price Crystal Palace at 10/1 to try and prise the striker away from QPR this January.