The 29-year-old striker will be allowed to leave St Mary’s for the right offer before tomorrow’s transfer deadline.
He will favour staying in the top-flight in a permanent deal despite interest in the Championship from Stoke and Aston Villa.
Wolves, Crystal Palace and Cardiff are trying to sign a striker before the window shuts and have been alerted to Austin being available.
The ex-QPR striker’s Premier League experience means he is likely to be a player who feature in the deadline-day mix.
He has two goals in eight Premier League starts this term but Hasenhuttl’s style of play will limit his chances in the second half of the season.
Austin has made 68 league appearances for the Saints since his £4million switch from QPR in January 2016 but is now surplus to requirements.
Saints signed Danny Ings from Liverpool in August 2018 and he has scored eight goals in 16 appearances since his arrival.
Austin scored in Hasenhuttl's debut home win against Arsenal in December.
Saints will only let Austin go on a permanent deal though, rather than a six-month loan.
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