One of the construction companies building the high-speed rail link HS2 between London and Birmingham could go into administration as soon as Monday (15 January).

Carillon, Britain's second-largest construction group which is also carrying out other government infrastructure projects, was described as being on the brink of collapse this weekend as its directors held last-ditch talks to save the company. It has debts of £1.5bn including a £587m pension shortfall.

Carillon won the contract to build tunnels, bridges and embankments along the first phase of the new rail link alongside Costain and Balfour Beatty in July, but eyebrows were raised about the troubled company even then as it lost three-quarters of its share price following a profit warning just one week earlier. Transport Secretary Chris Grayling said at the time that the company had given him "secure undertakings".

Former Labour Transport Secretary Andrew Adonis tweeted: "Carillion collapse raises big questions about Chris Grayling awarding them contracts long after they were in..."

Brandon Lewis, who has just been appointed Tory party chairman, told the BBC the government was keeping "a very close eye on this" as high-level government meetings are being held. Ministers have ruled out a financial bailout, but a rescue plan involving the contractor borrowing new funding from existing lenders is being considered. However, the government would have to guarantee payments at certain stages of public sector contracts.

A source told Sky News it was a "make-or-break weekend," adding: "Without that commitment of support from the government, administration is all but inevitable."

Carillon employs about 19,500 people in Britain and has numerous sizeable infrastructure commitments, as the second-largest supplier to Network Rail and maintenance provider for half of the UK's prisons. The contractor is also building the Aberdeen Bypass and schools across the country. It is also feared that 28,000 pension scheme members will face cuts to retirement payments if Carillon fails.

In a statement released after the stock market closed on Friday, Carillon said it was holding "constructive discussions with a range of financial and other stakeholders ‎regarding options to reduce debt and strengthen the group's balance sheet".