Jedinak's contract with Championship side Aston Villa runs out at the end of this season.
The 34-year-old would join as the inaugural marquee player if negotiations are successful and the bid is awarded an A-League license, reports The Sydney Morning Herald.
Jedinak previously played in the A-League for the Central Coast Mariners between 2006 and 2009, before heading to Europe.
Prior to his three-year spell with the Mariners, Jedinak played in south-west Sydney with Sydney United who he joined as junior before going on to captain the first team.
According to the report, Jedinak wishes to become a coach after his playing career is over and the offer would include a pathway to take up a future coaching role with the club.
The defensive midfielder played 79 times for the Socceroos, scoring 20 goals in an international career that included playing at three World Cups.
