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.
She called for an urgent task force, including employers and trade unions, to be set up to rescue Carillion's outsourcing contract and evaluate how the collapse of the company could impact on infrastructure projects, the public sector and the wider economy.
The debt-ridden builder has come up with a plan that would allow it to borrow new funding from existing lenders if the government agrees to guarantee payments at certain stages of public-sector contracts, with emergency talks with officials scheduled for Sunday, Sky said.
Carillion is holding crisis talks with United Kingdom government representatives on Friday, which Sky News said were aimed at safeguarding the more than 28,000 pension scheme members who face potential cuts to retirement payments should Carillion fail.
Carillion said that as part of its engagement with stakeholders, including banks, it is in constructive dialogue in relation to additional short-term financing while the longer term discussions are continuing.
As well as its Scottish projects, Carillion is a major supplier to the UK Government and a key contractor in the first phase of building the £56 billion HS2 rail line.
Senior civil servants from the Cabinet Office are due to attend an emergency summit that will include representatives from The Pensions Regulator (TPR), Pension Protection Fund (PPF), Carillion's pension trustees and an assortment of City advisers.
Earlier this week, Carillion presented a revised business plan to scores of lenders - but contrary to reports, this was not expected to produce an instant agreement with them.
A spokeswoman for Carillion said it met creditors on Wednesday but would not comment on reports of further talks.
The talks took place 24 hours after a meeting of ministers from across a multitude of Whitehall departments to discuss contingency plans for its collapse. Carillion had 924 million pounds of long term debt as of June 2017.
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The rescue plan shown to lenders on Wednesday includes handing back some loss-making contracts, revising the terms of others and potentially accepting financial support from the Government if it can not secure it from private sector sources.
A number of disposals aimed at raising cash, including that of its Canadian operations, are progressing more slowly than originally anticipated.
A spokesman added: "Carillion is one of three partners delivering the route".
Such a plan would leave its pension scheme, or the Pension Protection Fund, as a big shareholder.
Since then, the company has cleared out its executive team, including chief executive Richard Howson and finance director Zafar Khan.
Carillion's fight for survival is being led by interim boss and industry veteran Keith Cochrane, a former CEO of engineer Weir Group.
What does under-threat company Carillion do?
Warning against a Government bailout, he said: "I think what has to happen in this case is the contracts have to be kept going, supporting the supply chain and the tens of thousands of workers, and that can be done by the Government taking a lot of this in-house or re-tendering".