Carillion shares earlier plunged 30 percent to a new low after Sky News reported the company had put administrators on standby and the government said it had held a crisis meeting over the fate of the business - a major provider of public services employing around 43,000 people.
A person familiar with the matter also told Reuters that creditors did not like the plan put forward by the company.
However, Carillion said it remained in constructive talks over securing additional short term financing and that longer term discussions were also continuing.
Any agreement was likely to involve the raising of new capital and the conversion of existing debt to equity, which would result in "significant dilution to existing shareholders," it said in a statement.
Tensions around the 200-year-old company have been ratcheting up for weeks and on Thursday ministers overseeing everything from justice to transport, health and education met to discuss how they should respond to the possible demise of a business that plays a central role in British public life.
"Ministers did meet yesterday, there are ongoing meetings," a spokesman for Prime Minister Theresa May said. "We are monitoring this situation closely and will continue to do so."
One of many private companies to run public services in Britain, Carillion is fighting to survive after costly contract delays and a downturn in new business prompted a string of profit warnings and a first-half loss of more than 1 billion pounds ($1.4 billion).
Shares in Carillion closed down 29 percent at 14 pence, after touching a new low of 12.5 pence and compared with a price of 240 pence a year ago. Its market value of 64 million pounds compares with debt and liabilities of 1.5 billion pounds, according to analysts.
Any collapse would be felt across Britain and also in Canada and the Middle East where it has worked on landmark projects.
The company provides services to government departments including justice, health and education, and has built hospitals, roads and rail lines.
Spun out of Tarmac nearly 20 years ago and having bought Alfred McAlpine in 2008, Carillion has worked on key construction projects including London's Royal Opera House, the Suez Canal road tunnel and Toronto's Union Station.
In July last year it won contracts to build Britain's new High Speed 2 rail line, a key project that will better connect London with the north of England.
The GMB trade union called on the government to protect Carillion's workers and pensioners, but said the company should not be bailed out.
"Handing Carillion bosses a blank cheque bail out is completely unacceptable – company bosses should not be rewarded for failure with public money," it said in a statement.
The company met with creditors including RBS and Santander UK on Wednesday to ask them to consider a debt extension or roll-over in financing talks and it was expected to talk with the Pension Regulator on Friday.
Its pension deficit stands at around 580 million pounds.
The person familiar with the situation, who asked not to be named due to the sensitivity of the situation, said the government needed to get involved to help prop up the supplier. The Financial Times said the creditors rejected the deal.
Many of Britain's service providers have been hit in recent years after they took on work during the financial crisis at low prices for long-running, fixed-price contracts to keep work coming in.
The contracts left little room for delay or failure and have led to problems for groups including Capita, Mitie and Interserve.
Carillion's fight for survival is being led by interim boss and industry veteran Keith Cochrane, a former CEO of engineer Weir Group. New CEO Andrew Davies, head of family-owned builder Wates Group and formerly with defence company BAE Systems, joins on Jan. 22.
(Additional reporting by David Milliken, Lawrence White and Justin George Varghese; Editing by Paul Sandle and Mark Potter)
By Kate Holton and Andrew MacAskill