Football Federation Australia (FFA) are under orders from FIFA to widen representation in the Congress before the end of November or risk being replaced by a "normalisation committee" appointed by the global governing body.
At the heart of the dispute is the extent of representation in the Congress of the clubs from the professional A-League, which currently have just one of 10 votes, and the players' union (PFA), who are unrepresented at present.
The Congress elects members of the executive FFA board.
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Two days of intensive talks in Sydney attended by officials from FIFA and the Asian Football Confederation failed to deliver a resolution, however.
"A wide range of options has been robustly discussed over the past 48 hours," FFA Chairman Steven Lowy said in a statement.
"Everyone, including the FFA Board, A-League club owners, Member Federations and the PFA have shown willingness to move from their original positions and this has been noted by the FIFA/AFC delegation.
"FFA is hopeful that an agreement can be reached to enable the necessary procedural changes to achieve an expanded Congress by the end of November."
The chairman of the Australia Professional Football Clubs Association, which represents the clubs, placed the blame for the failure of the talks squarely at the door of the FFA.
"We are bitterly disappointed at not having reached consensus with our fellow stakeholders," Greg Griffin told local media.
"We are equally disappointed at the obstruction of the process by the FFA board."
The other nine votes in Congress go to representatives of states and territories and, while there is apparent agreement that the Professional Footballers Australia (PFA) should have a vote, the sticking point is how many the clubs get.
An FFA proposal for an "interim" Congress giving the 10 A-League teams two extra votes was rejected by FIFA in July and talks this week focussed on a proposal giving them five in total.
(Reporting by Nick Mulvenney, editing by Ian Ransom)
