Carillion is also involved in two UK-wide Ministry of Defence contracts for facilities management that cover nearly 20 Scottish sites including Dreghorn Barracks in Edinburgh.
Sky News reported that the approach is part of a contingency plan by Carillion as talks continue with bankers.
A source said it had "dipped the toe" and "had conversations" with alternative developers and service providers.
Carillion PLC (LON:CLLN) shares dropped by almost 30% in late afternoon trading on reports that its lenders have rejected the embattled construction firm's business plan, and that it has lined up an accountancy firm as a standby administrator.
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".
United Kingdom shadow business secretary Rebecca Long-Bailey said: "The collapse of Carillion could provoke a serious crisis".
Despite its being commissioned for a range of significant government and infrastructure contracts, Carillion is struggling under a £900m mountain of debt and a £590m pension deficit.
"The Government knows the disastrous consequences of a Carillion collapse so is doing all it can to avoid that happening".
Image The company also built the Tate Modern
"If the government is forced to institute a rescue package they need to also ensure that the supply chain is fully protected".
The Wolverhampton-based company - a major supplier to the Government and named among the firms awarded deals for the building of phase one of the HS2 rail line - is meeting lenders to discuss options to reduce net debt, recapitalise and/or restructure the group's balance sheet.
A spokeswoman for the government declined to comment on any specific meetings.
He said it was a "pretty messy situation", adding: "The situation is pretty bleak".
Transport Scotland said that Carillion had "no intention of withdrawing" from the AWPR project, and that the consortium delivering the route "remains committed to completing it in accordance with the contract". The long-awaited route is due to be finished this year following lengthy delays.
A spokesman for The Pensions 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".
A spokeswoman for the Pension Protection Fund said it was "aware of the discussions between the company, government and banks and, along with the trustees and the Pensions Regulator, will act as it always does to protect the interests of Carillion scheme members and levy payers".
"Handing Carillion bosses a blank cheque bail out is completely unacceptable - company bosses should not be rewarded for failure with public money", it said in a statement.
Carillion also said turnaround proposals on the table were likely to cost shareholders.
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