Watford and Southampton join Newcastle United and West Ham as the four clubs who have been linked with the 28-year-old, reports the Huddersfield Examiner.
Mooy is under contract until 2020, but with Huddersfield relegated to the Championship there are strong rumours that he could be on the move.
The Socceroos midfielder played 29 times in the Premier League this season, scoring three times and producing one assist.
Mooy joined Huddersfield in 2016, initially on loan from Manchester City, before signing permanently in 2017 for $15 million.
