The plans to raze and rebuild both the 80,000-seater stadium and the 44,000-capacity Sydney Football Stadium (SFS) at a cost of more than A$2 billion (£1.2 billion) were announced by the New South Wales government last November.
The Olympic Stadium was to be replaced by a 75,000-seater structure, possibly with a roof, at a cost of A$1.5 billion starting in 2019, with the construction of the new SFS getting underway next year and scheduled for completion by 2021.
The move attracted major criticism and an online petition calling for Premier Gladys Berejiklian's state government to scrap the project and invest the money in smaller, grassroots sports facilities has gathered more than 200,000 names.
The project, or at least the part of it involving the SFS, was set to be approved at a meeting of the state cabinet on Thursday but The Australian reported that it had been "pulled" from the agenda while the government considered is options.
A spokeswoman for New South Wales sports minister Stuart Ayres told Reuters on Wednesday that they "would not comment on cabinet processes".
A huge public relations offensive backing the stadium rebuilds was launched this week with rugby league, rugby union and soccer's governing bodies threatening that Sydney would lose major events if the plan foundered.
Australia has announced plans to bid to host the 2023 women's soccer World Cup and both men's and women's Rugby World Cups over the next decade.
(Reporting by Nick Mulvenney in Sydney and Ian Ransom in Melbourne, editing by Greg Stutchbury)
