A Downing Street spokesman also said the Government was monitoring the unfolding situation.
Carillion has put one of the big four accountancy firms on standby to oversee an administration of the construction giant in a further signal of the precarious state of its finances.
"It is too early to predict the outcome of these discussions but Carillion expects that any such agreement is likely to involve the raising of new capital and the conversion of existing financial indebtedness to equity which would result in significant dilution to existing shareholders", Carillion explained in a statement.
"Ministers did meet yesterday, there are ongoing meetings", he said.
Carillion is a major supplier to the Government and key contractor in the first phase of building the £56 billion HS2 rail line, but has seen its share price plunge almost 80% in the past six months after making a string of profit warnings and breaching its financial covenants.
The company provides services to government departments including justice, health and education, and has built hospitals, roads and rail lines.
Any collapse would be felt across Britain and also in Canada and the Middle East where it has worked on landmark projects.
In July a year ago it won contracts to build Britain's new High Speed 2 rail line, a key project that will better connect London with the north of England.
Carillion reported a first-half pre-tax loss of £1.15bn in September, while it announced just before Christmas that its lenders had agreed to defer a test of its borrowing agreements from 31 December to 30 April.
In a statement, Carillion said: "Suggestions that Carillion's business plan has been rejected by stakeholders are incorrect".
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.
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. The Financial Times said the creditors rejected the deal.
Apart from the NHS, Carillion has a contract for work on the HS2 rail link and is one of the leading suppliers of rail infrastructure services in the UK.
A spokesperson for the Pensions Regulator said the organisation remained "closely involved" in discussions with Carillion and the trustees of its pension schemes.
Its only asset sale since the crisis erupted has been to offload a portfolio of healthcare contracts to rival outsourcer Serco for £50m - against a broader forecast for disposal proceeds of £300m.
The contracts left little room for delay or failure and have led to problems for groups including Capita, Mitie and Interserve. New CEO Andrew Davies, head of family-owned builder Wates Group and formerly with defence company BAE Systems, joins on January 22.