Sky News also reported that the company has put accountancy firm EY on standby to oversee an administration if it is unable to secure a rescue deal.
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 company is the UK's second-largest construction company and a key government contractor.
Carillion's worsening health could put some of its 19,500 United Kingdom employees' jobs at risk.
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.
Carillion has a pension deficit of roughly £580m, although this figure would be expected to rise sharply if measured according to the cost of insuring its various retirement schemes on a full buyout basis.
It said the firm remained in constructive dialogue about short term financing while "longer term discussions are continuing".
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".
Shadow business secretary Rebecca Long-Bailey said on Friday the Government must "stand ready to bring these contracts back into public control, stabilise the situation and safeguard our public services".
By 4.00pm, Carillion shares were down 29.4%, or 5.88p to 14.11p, having hit a low of 12.5p after the reports emerged, after being more modestly lower this morning.
Ministers met Thursday to discuss the issue, and there will be "ongoing meetings", Blain said.
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.
A spokesman for the Pension Regulator 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 general secretary of the RMT rail union, Mick Cash, said Carillion's workers "should have protection and guarantees from the government, including an assurance that operations will be directly transferred over to Network Rail" if it goes bust.
"We will not comment further unless it becomes appropriate to do so".