The department has been forced to consider this option because of the shortage of skilled labour for PFI projects and the difficulties that employers face in ensuring that foreign staff are not working in the UK illegally. If the Home Office sets up an agency it could write its own standards for vetting workers.
Under the plan, details of all foreign workers entering the UK are to be collected and stored as part of the CSCS scheme.
It is understood that employers are to be encouraged to identify all foreign workers on sites to ensure they are here legitimately.
In a linked development David Blunkett, the home secretary, launched the Asylum and Immigration Bill in the Queen's speech on Wednesday.
To pave the way for the introduction of the labour agency, George Brumwell, general secretary of UCATT, is being lined up as chairman of the CSCS for when Tony Merricks steps down on 22 January.
Brumwell, who will retire from UCATT next year, is being asked to raise the profile of the CSCS and to oversee plans to manage the allocation of foreign workers to sites.
A Whitehall source said the idea was only in its infancy but had the attraction that it could supply the government with the skilled labour required to deliver the PFI programme while clamping down on illegal working.
He said Brumwell would be the perfect person to head the scheme: as a former union leader he could be relied upon to ensure that the rights of foreign workers were not ignored, he would have contacts with contractors and the political know how to hold his own with government departments.
The source said: "The idea is to construct a scheme that creates a formal route for all foreign workers entering the UK construction industry. The idea would be to match the competences and skills of the workers on the agency's books with the needs of this or that contractor."
He said that once the scheme was in operation it could be used to vet foreign workers, spotlighting those who were not here legitimately.
He said: "It could allow a central agency to deploy skilled foreign workers to where they are most urgently needed – that is, the government's PFI programme."
The Home Office's plan would also help to solve the construction industry's poor record for recruiting entrants from an ethnic minority and women.
A Home office spokesman said: "We are currently considering the proposals in light of the decision to prepare for the introduction of a national identity card scheme and in light of other policy decisions."