The Australian is a free agent after leaving Shanghai Port and is well known to Ange Postecoglou during his time as Socceroos manager.
Fabrizio Romano has reported Mooy will sign a contract for the season with an option for an extension.
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Hide AdThe 31-year-old midfielder could be viewed as a replacement for Tom Rogic who left the club this summer.
Mooy can play different midfield roles but is a predominantly forward-thinking player. His goalscoring form for Melbourne City saw him recruited by Manchester City but would never play a game for the English champions, impressing on loan at Huddersfield who would sign him for an initial £8million.
He has also played for Brighton & Hove Albion before making the move to China.
Mooy’s first steps in first-team football were at St Mirren, who signed him from Bolton Wanderers. He played 30 times for the Buddies before returning to Australia.
Postecoglou, after Saturday’s friendly draw with Blackburn Rovers, revealed he expects signings this week and that the club were close to the “end point” of their recruitment.


The Australian had previously addressed the links with Mooy while in Czech Republic during pre-season.
He said: “Aaron’s a fantastic footballer, somebody I know really well. I guess he’s getting linked with us.
“I’m sure he’ll get picked up, he’s a good player, a talented player.
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Hide Ad“He’s another footballer who is very much talented and very much in my range. But, that doesn’t mean we’re going to bring him in, no.”