Reports suggest Carillion is in financial crisis following the announcement of net debts between Â£875m and Â£925m, and a pension shortfall of Â£587m.
The company, which has offices in Sheffield and Leeds, is trying to reach an agreement with creditors and it is understood talks with high-ranking Government officials from the justice, transport and business departments are taking place this morning in a meeting chaired by the Cabinet Office.
The firm is a key Government contractor for projects including the HS2 high-speed rail scheme, schools and prisons.
It has a call centre in Broad Street West that employs 250 people and is the main contractor on a Â£19m contract – part funded by business – to build flood defences along a five-mile stretch of the River Don in the Lower Don Valley.
Carillion is also building the much-delayed tram-train project to connect Sheffield, Meadowhall and Rotherham. The project - the first of its kind in the UK - was originally due to be completed in 2015 but is still not finished and will cost around Â£75 million - after an initial estimate of Â£15m in 2012. Liberal Democrat leader Sir Vince Cable MP said the government must not bail out the construction company, which is the second largest in the UK.
He said: "They've got to force the shareholders and indeed the creditors, the big banks, to take losses, and then the government can take responsibility for taking the contracts forward and making sure they are delivered."
Jon Trickett MP, shadow minister for the cabinet office, called on the government to take contracts back into public control, describing its relationship with the Carillion as a "failing ideological project."
He added: "It has been clear for months that Carillion has been in difficulty but the government has continued to hand over contracts to the company."
The company is headquartered in Wolverhampton and employs 43, 000 people globally.
Business analysts have highlighted three public finance initiative schemes, the Â£350m Midland Metropolitan hospital in Birmingham, the Â£335m Royal Liverpool University hospital and the Â£745m Aberdeen bypass, as reasons behind the financial woes as the schemes are late and over budget.
Several months ago the firm had won a bid to design and build part of the HS2 route.
Amid concerns about the future of the company last summer, a Carillion spokesperson gave reassurances that all existing contracts were continuing as normal, including in Sheffield.
Carillion issued a statement on Friday and today said they are not making any further comment at this time.
The statement said: "Carillion met with representatives of its creditor groups to present its business plan on 10 January 2018.
"Further to this presentation, Carillion continues to engage in constructive discussions with a range of financial and other stakeholders regarding options to reduce debt and strengthen the Group’s balance sheet.
Suggestions that Carillion’s business plan has been rejected by stakeholders are incorrect.
"It is too early to predict the outcome of these discussions but Carillion expects that any such agreement is likely to involve the raising of new capital and the conversion of existing financial indebtedness to equity which would result in significant dilution to existing shareholders.
"As part of its engagement with stakeholders, Carillion is in constructive dialogue in relation to additional short term financing while the longer term discussions are continuing.
"The board remains focused on seeking to deliver an outcome that will ensure that the group emerges considerably strengthened and able to continue delivering excellent service to its many public and private sector customers."