Carillion now employs around 20,000 workers in the UK.
It is understood the Scottish Government has put contingency plans in place to plug the gap if Carillion collapses, covering both its facilities management and construction services.
In 2016 the Wolverhampton-based company, which employs 43,000 people globally, had sales of £5.2bn and until July boasted a market capitalisation of nearly £1bn.
The Guardian's website reported shadow business secretary, Rebecca Long-Bailey, as saying: "The collapse of Carillion could provoke a serious crisis".
Bosses at Carillion have appealed for a state-backed rescue, telling ministers that its survival rests on a bail-out of the firm's most troubled contracts.
A TPR spokesperson said: "We have been and remain closely involved in discussions with Carillion and the trustees of the pension schemes as this situation has unfolded".
The company provides vital services to hundreds of schools.
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Ministers met Thursday to discuss the issue, and there will be "ongoing meetings", Blain said.
The reported that David Lidington, who was moved to the Cabinet Office as part of Prime Minister Theresa May's reshuffle this week, convened the meeting with Business Secretary Greg Clark, new Justice Minister Rory Stewart, new Transport Minister Jo Johnson and Liz Truss, Chief Secretary to the Treasury.
Her views were echoed by Unite union assistant general secretary Gail Cartmail, who said: "The government must consider all options while the future of Carillion hangs in the balance, including bringing contracts back in-house".
The Government is notoriously slow at settling bills with contractors, and frequent delays have exacerbated Carillion's cash crunch.
The company has been pushed to the brink by cost overruns that forced it into a string of profit warnings a year ago and left it on course to breach the terms of its bank loans.
"We are committed to maintaining a healthy supplier market and work closely with our key suppliers".
Adding to the pressure on the small cap firm - which issued three profit warnings in less than six months previous year and has seen its market value collapse by 90% - was a recommendation from broker Peel Hunt to sell the stock ahead of forthcoming newsflow.
They added: "The PPF is aware of the discussions between the company, government and banks and, along with the trustees and TPR, will act as it always does to protect the interests of Carillion scheme members and levy-payers".