Reports in the UK claim that Brighton have been honing in on the Huddersfield Town midfield maestro, who has been linked with a number of Premier League clubs this off-season.
Seagulls coach Graham Potter is said to be on the lookout for midfield reinforcements with Mooy reported to be his number one target.
The Sydney product's future at Championship club Huddersfield Town has been the subject of much conjecture after the side were relegated from the English top flight in May.
It is understood the Socceroos veteran has been hopeful of move to a Premier League club this season but long standing interest from Newcastle United, Bournemouth, West Ham United and Watford has not eventuated into any solid bids.
Huddersfield would be looking to cash in on arguably their most valuable asset and are believed to have set a transfer fee in excess of A$20 million for Mooy.
The Terriers bought Mooy for A$17 million from Manchester City two years ago, after a successful loan stint at the club helped their promotion to the Premier League.
Mooy played the full 90 minutes in Huddersfield's Championship opening round 2-1 defeat to Derby County on Tuesday (AEST).
The Former Western Sydney Wanderers and Melbourne City midfielder is not the only Aussie likely to join a new club before the transfer deadline.
Massimo Luongo is expected to depart Queens Park Rangers for a rival Championship club, while Mile Jedinak is also on the lookout for a new club after he was released by Aston Villa two months ago.
The transfer window closes at 5pm in the UK on Thursday (2am Friday morning AEST), ahead of the start of the 2019-20 Premier League campaign the following day.