Honda will quit Formula One on Friday, BBC Sport understands.
The Japanese company hopes to sell its team, which costs £200m a year to run, but is prepared to close the team early in 2009 if no buyer is found.
Sources told BBC Sport the team were "optimistic" they would continue, but an investor had yet been found.
According to the Reuters news agency, team bosses Ross Brawn and Nick Fry fear Honda could close the Brackley-based operation within weeks.
According to a Reuters source, Brawn and Fry told a meeting of the Formula One Teams' Association: "They have a month to find a buyer, otherwise they are closing the team."
Honda appointed Brawn, the man who masterminded seven world titles for Michael Schumacher, as their team principal prior to the start of the 2008 season.
Briton Jenson Button, who drives for the Honda team, will be left unattached for the 2009 season if the team folds, though some places with mid-ranking teams remain.
After recently cutting road vehicle production as a response to the global economic crisis, Honda is expected to make an announcement regarding the team's future early on Friday.
A notoriously expensive sport in which to compete, F1 teams have spent recent months in intensive discussions over cost-cutting measures.
Max Mosley, president of world motorsport governing body the FIA, recently urged teams to find ways to reduce costs.
"Formula One is becoming unsustainable," said Mosley in July.
"The major manufacturers are currently employing up to 1,000 people to put two cars on the grid. This is clearly unacceptable at a time when all these companies are facing tough market conditions."
In October, a deal was reached to reduce costs for smaller teams in 2009 and 2010.
Considered a major player within Formula One, Honda bankrolls more than 800 staff at the team's Northamptonshire base and has the largest budget in the sport.
"I am told that for £1 you can now buy the Honda F1 team," said BBC sports news correspondent Adam Parsons.
BBC Radio 5 Live's F1 commentator, David Croft, said Honda's withdrawal could have profound consequences for the sport.
"This has serious implications for F1, not just because there will be only 18 cars on the grid," said Croft.
"It's the start of the sport as a whole feeling the pinch. Williams are reported to be in financial difficulties, Toyota are trimming down their budget as well.
"Honda are a car company whose sales have dropped by 41% in the last quarter, they're closing their Swindon factory for two months at the start of next year, and obviously feeling the pinch on a global scale."
In November, Honda announced it would build fewer cars in Japan, Europe and the United States to reflect bleak economic prospects in the vehicle manufacturing industry.
Sales of new cars in the UK suffered their biggest monthly drop in 28 years, while carmakers Ford, GM and Chrysler have asked the US Congress for multi-billion dollar loans to guarantee their survival.
The last team to leave Formula One were Honda-backed minnows Super Aguri, which folded for financial reasons in April.
Honda's own F1 team endured a deeply disappointing 2008 season on the track, earning just 14 points, leaving them the lowest of the nine points-scoring teams.
Button found himself ranked 18th in the drivers' list, contributing only three points.
Only four drivers, each without a point to their name, ranked below him. Team-mate Rubens Barrichello earned the remaining 11 points.
Honda initially entered F1 as a constructor in the 1960s, withdrawing at the end of 1968.
The company returned to F1 in the 1980s as an engine supplier and then purchased a stake in the BAR team from British American Tobacco (BAT) in 2004.
Honda bought out BAT in 2005 to form the Honda team for the 2006 season.
While the team finished fourth in the 2006 constructors' championship, they have subsequently struggled to make an impact.
The 2009 Formula One season begins on 29 March, in Australia.
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Statement from Takeo Fukui(Honda Motor CEO)
We, Honda Motor Co., Ltd., have come to the conclusion that we will withdraw from all Formula One activities, making 2008 the last season of participation.
This difficult decision has been made in light of the quickly deteriorating operating environment facing the global auto industry, brought on by the sub-prime problem in the United States, the deepening credit crisis and the sudden contraction of the world economies.
Honda must protect its core business activities and secure the long term as widespread uncertainties in the economies around the globe continue to mount. A recovery is expected to take some time.
Under these circumstances, Honda has taken swift and flexible measures to counter this sudden and expansive weakening of the marketplace in all business areas. However, in recognition of the need to optimize the allocation of management resources, including investment regarding the future, we have decided to withdraw from Formula One participation. We will enter into consultation with the associates of Honda Racing F1 Team and its engine supplier Honda Racing Development regarding the future of the two companies. This will include offering the team for sale.
In its third era of Formula One activities, Honda has been participating in Formula One races from the 2000 season, initially with BAR, by adopting a new format of jointly developing racing machines. Subsequently, in a move to meet the changing environment surrounding Formula One, we switched to running a 100% Honda-owned team commencing with the 2006 season.
Surmounting many challenges, the Honda Team achieved a Grand Prix victory in 2006, enabling Honda to receive overwhelming support from Honda fans around the world that were looking forward to greater success. It, therefore, has been an extremely difficult decision for us to come to this conclusion without having been able to fully meet the expectations of our fans.
By making the best of what we have learned during these times of economic turmoil, coupled with the spirit of challenge gained through active participation in racing, we intend to continue with our commitment in meeting new challenges.
Finally, we would like to take this opportunity to sincerely thank our fans and all those who have supported Honda's Formula One efforts, including everyone in the world of Formula One.
Thank you very much.
Takeo Fukui
President and CEO
Honda Motor Co., Ltd.