The FFA convened discussions in Sydney on Friday between state bodies, A-League clubs and the players' association.
The talks were centred on reforming FFA's congress, which elects the FFA board and sets a path for the sport in Australia.
With 10 members - nine state and territory bodies and an A-League representative - Australia's congress is the smallest of any FIFA-affiliated nation, leading the world body to request broader representation.
FIFA set the reform request, given the small make-up of the congress and the transition of power in November 2015 from previous chairman Frank Lowy to his son Steven.
The reform challenge has been taken up with gusto by power-starved groups.
A-League clubs are hungry to gain more seats at the table, believing their investment earns them the right to a louder say in how the sport is run.
Other interests - including the players, women's football and referees - would also like more influence.
FIFA had put a March 31 deadline on the request, a date that looks unlikely to be met after Friday's stalemate.
At the very least, the ongoing power play will cast a shadow over the crunch 2018 FIFA World Cup qualifier with United Arab Emirates on Tuesday week (March 28) in Sydney.
It's understood FFA hasn't closed the door on reaching a resolution on a new Congress model, which will need to be signed off at an extraordinary general meeting.
While eight of the Congress must agree to the reforms for them to pass, a new model will need to satisfy other parties - particularly A-League clubs - to end ongoing hostilities.
The FFA board has just 14 days to pull off that delicate negotiation.
"Everyone was able to explain their position today as part of a frank and very constructive discussion," Lowy said in a statement.
"There was discussion on many points, including the relevance of intended changes to the ownership and operating model of the Hyundai A-League to the make-up of an expanded Congress.
"On the few matters where different views are held, everyone at the meeting agreed to go back to their own boards to consider the path forward.
"Discussions will continue next week."
It's understood parties to the discussions agreed to keep the content of the talks confidential, contradicting previous pledges for a transparent process.