It reported revenues of more than £5bn in 2016, and is one of the largest construction service multinationals in the UK.
Administrator firms PwC and EY were also reported to have been put on standby as talks about the firm's future carry on.
Gail Cartmail, Unite assistant general secretary, said Carillion's workforce was being "held hostage by the whims of the market".
Carillion's major projects have included "the doughnut" - the iconic circular office building of the UK's Government Communications Headquarters (GCHQ) - completed in 2003. "The collapse of Carillion could provoke a serious crisis".
Carillion, which is struggling under £900 million of debt and a £590 million pension deficit, denied the business plan had been rejected by stakeholders, but added that a restructuring could result in a debt for equity swap.
Sir Vince, a former business secretary, told BBC Breakfast: "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".
The Wolverhampton-based group is the second-largest supplier to Network Rail and maintains approximately half of the UK's prisons as well as roughly 50,000 homes for the Ministry of Defence.
The company provides vital services to hundreds of schools.
Shares, down 90 pct since co's first profit warning in July, fall as low as 12.5 pence around noon in London.
"Without that commitment of support from the government, administration is all but inevitable", the source said.
He said it was a "pretty messy situation", adding: "The situation is pretty bleak". It is also a key contractor on the £56bn HS2 rail project. The long-awaited route is due to be finished this year following lengthy delays.
In a note to clients, Peel Hunt's analysts said: "We suspect that given its mounting liabilities, recent press comment, growing customer worries and supply chain hesitancy that Carillion will be forced (by the banks) to accelerate its financial restructuring".
"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".
"Labour urges the Government to stand ready to intervene and bring these crucial public-sector contracts back in-house in order to protect Carillion's employees, pension holders and British taxpayers".
Last month, Carillion said it received all necessary consents to defer the test date for both its financial covenants from December 31 to April 30, 2018, and that it was continuing constructive talks with stakeholders on options for cutting net debt and recapitalizing.