The Australian was signed by the Citizens in 2016 from sister club Melbourne City, before being loaned to Huddersfield Town for the 2016-17 season.
Mooy's Huddersfield Town move was made permanent at the start of last Premier League season with the Terriers breaking their transfer record to sign the tireless midfielder for £10 million (A$17.9m).
However, as part of the deal Pep Guardiola's side are believed to have included a buy-back clause for Mooy valued at £20 million (A$35.8m) which they are considering activating, according to ESPN FC.
After an impressive first season in the English top flight, and a solid showing in Russia with the Socceroos, Manchester CIty feel the Australian could be a quality addition to bolster their already star-studded midfield stocks.
Manchester City are not the only side looking to sign Mooy this transfer window with The World Game reporting West Ham, Everton and Southampton are also sizing up a potential move for the 27-year-old.
While no concrete offers have been tabled yet, it’s likely the Terriers would demand a huge fee for Mooy but they would be powerless to stop him leaving if City activate the buyout clause in his contract.
Having made a seamless transition to the Premier League, Mooy missed just two league games last season while spearheading Huddersfield’s survival act, netting four goals and three assists.
Mooy, who is contracted until mid-2020, has publicly stated that he is happy in Huddersfield, flourishing under the tutelage of coach David Wagner.
However, he is ambitious and there is no question that he would jump at the chance to join Guardiola's record breaking Premier League side as well as the prospect of Champions League football.