The 27-year-old midfielder impressed for Huddersfield in the Premier League last season, making 36 league appearances across the season.
The combative midfielder, who finished as one of the Premier League's top tacklers last season, has also impressed this summer for Australia in their World Cup campaign.
Mooy moved to Manchester City in 2016 from the club's sister side Melbourne City but never played a game for the team, before being loaned to Huddersfield for the 2016-17 season.
After an impressive Championship season, David Wagner's Terriers side made Mooy's move permanent in a deal rising to £10m. As part of that deal, City included a £20m buy-back option.
According to reports, Pep Guardiola is interested in activating that clause to bring the former player back to the Etihad.
Mooy is understood to be in high demand this summer, with Everton, West Ham and Southampton all also weighing up moves for the Australian as they look to bolster their midfield options ahead of next season.
Huddersfield are also known to be desperate to keep hold of their midfield maestro. However, should Manchester City chose to activate their buy-back clause, then Huddersfield will be powerless to retain the player's services.
Mooy only registered four goals and three assists across the Premier League season, though despite the stats played a key part in controlling and creating chances from the Terriers midfield.
The Australian midfielder has been capped 37 times for his senior national team, scoring five times, and played every minute of Australia's three World Cup group games this summer.