On Friday, the firm dismissed reports lenders had rejected a critical restructuring plan, saying it remained in "constructive discussions" with its creditors.
The government, the Pensions Regulator and representatives from the firm held crunch talks to discuss the firm's options on Friday.
A Government spokeswoman said: "Carillion is a major supplier to the Government with a number of long-term contracts".
It has previously been reported that EY is on standby for an administration.
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.
Ministers from the Justice, Transport, Culture, Health, Education and Communities departments and ministries were also present, the Financial Times reported.
It is also the second largest supplier of maintenance services to Network Rail.
The general secretary of the RMT rail union, Mick Cash, said Carillion's workers were "not responsible for the crisis".
Unions have urged Westminster to step in to protect 19,500 jobs that are now at risk, with Unite insisting "all possible options" must be considered - including bringing contracts in-house.
Nike's Team USA Medal Stand Collection for 2018 Winter Olympics
Intel TrueVR "pods" at each event will create a 360 degree virtual environment where viewers can watch. Team USA competes at the Winter Olympics in Pyeongchang , South Korea, starting February 9th.
Arsene Wenger backs Ainsley Maitland-Niles to replace Francis Coquelin in midfield
Coquelin spoke to former Arsenal team-mates Shkodran Mustafi, Nacho Monreal, Hector Bellerin and Santi Cazorla about the move. The first player to officially leave Arsenal this January transfer window is not Alexis Sanchez, but Francis Coquelin .
Future human outposts could be sustained by Mars' ice caps
Water ice can be used, of course, for life support as well as for making fuels for surface and space vehicles. They exist as pure water ice today, with rock and dust cemented in layers throughout it.
The company held talks with its lenders and advisers in London on Wednesday.
They added: "Based on our current trading assumptions (Dec' 18 EBITDA £188m with material downside risk) and our estimates of the mounting debt ( £1.1bn), likely additional supply chain funding/working capital unwind ( £300m) and pension liabilities (£600m), we now see no equity value".
The firm is now under investigation by the Financial Conduct Authority over the "timeliness and content of announcements" made between December 2016 and July 2017.
Cabinet Office minister David Lidington hosted the summit of senior figures including Business Secretary Greg Clark and Chief Secretary to the Treasury Liz Truss.
The company is fighting net debts of more than £900 million, following a crisis sparked in July previous year when it issued a profit warning.
The firm has seen its share price plunge almost 80 per cent in the past six months after making a string of profit warnings and breaching its financial covenants.
The UK Government said a ministerial meeting to discuss the crisis took place on Thursday, with a spokeswoman adding: "We are carefully monitoring the situation while working to ensure our contingency plans are robust".
A Government spokesperson repeated a statement given to Sky News last weekend which said it was "committed to maintaining a healthy supplier market and work closely with our key suppliers".
"We will not comment further unless it becomes appropriate to do so".