The 31-year-old is a free agent this summer and Celtic boss Ange Postecoglou wants him in Glasgow for the new season.
Celtic have accelerated talks with Mooy and Postecoglou is now set to secure the services of his countryman as he continues to strengthen his squad.
The Bhoys have now all but sealed the deal for the midfielder and he could be announced by the club on Monday.
Mooy’s last club were Chinese outfit Shanghai Port and he has headed back to Scotland to be with his Scottish wife and family.
The 31-year-old Australia international has played his football in Scotland before, having enjoyed a stint with St Mirren between 2010 and 2012.
Mooy signed for Shanghai Port in 2020, the Chinese club having snapped him up from Premier League side Brighton.
Now Mooy will add to Postecoglou’s options ahead of a season where Celtic have Champions League group stage football on the table.
