Holden has made the decision to pull out of Australia as early as 2016, according to senior Government ministers.
The ABC has been told the announcement was supposed to be made this week but has been put off until early next year.
Holden says discussions with the Government on its future are continuing, and it says it does not respond to speculation.
Industry Minister Ian Macfarlane says he has spoken to Holden and they have denied the reports.
The Federal Opposition has warned Holden would make the decision before Christmas if the Government did not announce an assistance package for the industry before then.
The Government has previously said it would wait for the findings of a Productivity Commission inquiry, due in March.
However, one source has told the ABC that Holden wants to leave Australia, regardless of any assistance package.
Holden closure would cripple automotive industry
Research released last month suggested that Holden's closure would cost the South Australian economy $1.24 billion and 13,200 jobs alone.
The Australian Manufacturing Workers Union (AMWU) says Toyota would be likely to follow suit, meaning the end of the Australian automotive industry.
In that case, up to 50,000 jobs could be lost across the country, with second and third-tier suppliers also forced to close their operations.
Ford announced in May it would close its Australian operations by October 2016.
Opposition industry spokesman Kim Carr says the revelation exposes a battle between government ministers who want to save the car industry and those who do not think it should be propped up
"What we're seeing here is a struggle being played out between the wets and the dries inside the Liberal Party and they think they can use the Australian automotive industry as a plaything in this battle," he said.
He says the Government cannot afford to wait for the Productivity Commission report and called for direct intervention from Prime Minister Tony Abbott.
"There is an urgency about this. We can't wait to March. There needs to be a serious intervention by the Prime Minister," he said.
"I frankly cannot understand why they have not had a delegation to Detroit by now to discuss these questions with the global leadership of General Motors.
"What we are looking at is this Government's indolence leading to a situation where we are seeing the collapse of the Australian automotive industry."
South Australian Premier Jay Weatherill says he spoke to Mr Macfarlane after the story surfaced last night and he and Holden denied the reports.
Mr Weatherill says the story has exposed deep divisions in the Coalition over the industry's future.
"This amounts to a massive split within the Federal Liberal Government and one which is an incredibly destructive one for the future of Holden and incredibly upsetting for those tens of thousands of workers in South Australia and across the nation who rely on the car industry for their future," he said.
No mention of closure from Holden CEO
The AMWU's John Camillo says Holden chief executive Mike Devereaux made no mention of a closure when he addressed workers at the company's Elizabeth plant in Adelaide yesterday.
"[Mike Devereaux] never mentioned anything in regards to any announcement or any discussion of closure," he said.
"He just indicated to workers he will be continuing his role as CEO of Australia until February next year until he gets a replacement.
"He indicated a decision will be made by GM in Detroit whether Holden stays or not. Then went on to talk about the Productivity Commission.
"I find it strange he addresses all the workers, doesn't indicate in regards to closure or speculation, and all of a sudden there is discussions or talks about a senior minister having understandings of these ceasing operation in Australia.
"At this stage we have to treat it as speculation, but it is up to the senior executive at Holden to allow the workers to be the first ones to be told if there is any truth in this speculation of Holden ceasing operation by 2016 or 17."
Mr Camillo says Holden's closure would have a catastrophic effect on Australian manufacturing and Toyota would follow suit.
"I don't think [Toyota] can sustain such small supplies in Australia to produce cheaper parts for them to continue producing here in Australia," he said.
"We will see the closure of the automotive industry within a few years."
Mr Devereux has been promoted to a position with parent company General Motors in China and was meant to finish up in Australia this month.
A Holden spokesman says the process to find Mr Devereux's replacement to head Australia's operations is taking time and he will now remain managing director well into the new year.
Mistake for Coalition not to commit assistance: Xenophon
Independent Senator Nick Xenophon says the nation needs to rally behind the car industry.
"This is shocking news just before Christmas," he said.
"I'm still hoping against hope that General Motors will reconsider.
"If they don't, as a nation we need to rally behind this industry to make sure it can survive, any job losses are minimised and we can look to the future without General Motors."
Senator Xenophon says there will be political recriminations, and wants to hear from Mr Macfarlane.
"I think a mistake has been made by this Government for not committing the money the former government did," he said.
"Right now we need to work together as a nation to save not just the precious jobs at Holden, but 50,000 jobs across the country relying on manufacturing."
Holden revealed in April that it has received $2.17 billion in Federal Government assistance in the past 12 years.