Mooy has yet to comment on his future and is currently still training with the Terriers, who are preparing for a Championship campaign after two seasons in the Premier League ended in relegation.
The Australian international has been one of Huddersfield's most important players since joining on loan from Manchester City in 2016 and subsequently signing permanently in 2017 for £10 million.
He has scored 11 goals and made 15 assists in 119 appearances for the Terriers across all competitions.
Mooy's contract expires at the end of the 2019-20 season with Town having the option to trigger a 12-month extension at this time.
Several Premier League clubs have been linked with the Socceroo since the end of the season, including Newcastle United, Wolves, West Ham and Southampton.