The firm is struggling under a £1.5 billion mountain of debt and plunging share prices, with lenders reportedly rejecting a proposed rescue plan.
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".
The government, the Pensions Regulator and representatives from the firm held crunch talks to discuss the firm's options on Friday.
Carillion is the UK's second-largest construction company and employs 43,000 people globally.
Mick Cash, general secretary of the Rail, Maritime and Transport (RMT) union, called for protection for workers "caught in the middle of this financial meltdown at Carillion".
A government spokeswoman said it has been monitoring the situation to ensure its "contingency plans are robust".
In addition to its rail operations, Carillion also manages almost 900 schools, provides services to the NHS and works with National Grid.
Unite assistant general secretary Gail Cartmail, said: "The Government must consider all options while the future of Carillion hangs in the balance, including bringing contracts back in-house".
Ministers have held crisis talks over a troubled company that hundreds of schools rely on for vital services, after questions were raised about its future.
"We are committed to maintaining a healthy supplier market and work closely with our key suppliers".
Carillion also has major contracts to supply facilities management at 83 military sites in Scotland, as well as a 28-year contract managing the "elderly beds facility" at Glasgow's Queen Elizabeth University Hospital.
It comes as the Government, pension authorities and stakeholders met on Friday in an attempt to thrash out a rescue package for the firm which would help it avoid collapse.
The company is fighting net debts of more than £900 million, following a crisis sparked in July past year when it issued a profit warning.
Its share price plummeted 90 per cent after announcing its first profit warning in July previous year.
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.
A spokesman for the Scottish government said: "We continue to liaise with United Kingdom government colleagues to monitor and mitigate service risks associated with Carillion's financial situation".
"We will not comment further unless it becomes appropriate to do so".