The CrossRail project was shelved by the Conservative government three years ago because it was felt to be too expensive.
The consortium is led by Groupe GTM, the third largest European construction company, with an annual turnover of pounds 4.5bn.
Jean Hervot, managing director of Groupe GTM, said: "We are in talks with the Corporation of London, and we are looking at the figures to see whether we want to take this project further. Our conclusions will be made within the next few months."
The Corporation, which owns much of London's Square Mile, confirmed that it is about to select a financial institution to scrutinise its business plan. In it, the Corporation argues that CrossRail would cost pounds 2.4bn and would yield 9 per cent for investors after 30 years. This figure could rise to 19 per cent, it says, once advertising and property revenue from retailers is included.
According to the property magazine Estates Gazette, other companies involved include the airports operator BAA, the design and construction group Ove Arup, the quoted City property company Greycoat, and consultant engineers Mott McDonald.
The parties attended a meeting last month organised by the City, the magazine said.
However, a spokeswoman for BAA, which owns and operates the new Heathrow Express train service from Paddington, said: "There are rumours in the City, but there is nothing that we are involved with."
Ove Arup produced a document for the Government in 1996 suggesting small- scale alternatives to CrossRail including a plan now adopted by Railtrack.
Railtrack last month told the Commons Transport Select Committee that it wanted to run commuter trains along the shallow lines of the London Underground: the Circle, District, Metropolitan, Hammersmith & City and East London lines.
Railtrack is bidding to take over the lines under the Government's public/private partnership.
This could provide a cross-London service at a fraction of the cost, as minor signalling improvements would allow Railtrack to run direct services from say Aylesbury in Buckinghamshire to Southend in Essex - a journey that currently requires changing trains three times.
A Railtrack spokesman said he was not aware of any approach to the company by GTM. He said CrossRail had been handed over to Railtrack by the Government but was on the "back burner".
He said most of the available resources for such projects were currently committed to building the Jubilee Line Extension, and that London Underground was also keen to go ahead with the planned Chelsea-Hackney line.
The CrossRail project would connect Heathrow, Reading and Bristol trains entering Paddington main line station to Bond Street, Tottenham Court Road, Farringdon and Liverpool Street in the City.
Joe Weiss, the Corporation of London's transportation and highways director, said Railtrack's plan to run mainline trains on the Tube was flawed because it failed to give commuters extra rail capacity.
"CrossRail will create desperately needed new capacity. If this scheme doesn't go ahead, the vitality of central London will be put at risk," he said.
"If it does go ahead, the opportunities for property developers and enhancement of central London property values will be immense."Reuse content