The Seagulls have struggled this season under the guidance of Sami Hyypia and they are desperate to improve their squad to help them avoid the drop.
Austin has apparently been identified as a player who would add steel and presence to their midfield and they have been tipped to table an offer for the Jamaican international at the next possible opportunity.
The powerful central midfielder is a first-team regular for the Whites and has made 15 appearances in all competitions this season.
He has, however, fallen out of starting contention more recently, with most of his appearances coming as a substitute.
Brighton may be hoping to take advantage of the uncertainty around Leeds at the moment. The club announced huge losses for the previous financial year this week and they are said to be aiming to trim their squad to avoid a repeat this time around.
Current Whites boss Neil Redfearn has insisted that he wants to trust the youngsters and as Austin is heading towards his 30s there is a question of whether he fits into the side's selection policy.
Austin remains a divisive figure at Elland Road, with many admiring his power and drive in midfield and others feeling that his distribution is unreliable.
Austin has been at Leeds since 2012, making 94 appearances for the Yorkshire outfit.