Mooy enjoyed a superb debut season for City, winning the club's Player of the Year award with seven goals from 25 appearances, after arriving from Western Sydney Wanderers.
The central midfielder has previously been on the books at UK clubs St Mirren and Bolton Wanderers, and could be on his way back to Europe after his agent, Paddy Dominguez, admitted Mooy has been attracting interest from overseas.
"Aaron is under contract with Melbourne City. As always with a player of Aaron's quality there is continuous interest in him both domestically and internationally," Dominguez said.
"We have had some discussion with Melbourne about the possibility of extending his stay there and will continue that dialogue in private and in good faith."