The Minister for Transport, Mr Brennan, is expected to opt for a part-underground metro link to Dublin Airport costing at least €2 billion rather than a cheaper rail spur off the Sligo line.
Mr Brennan will be bringing his proposals to the Cabinet as early as next month following an analysis of the alternatives by the Rail Procurement Agency (RPA), which is charged with overseeing the project.
The RPA submitted a "business plan" for the metro line to the Minister last November, estimating the cost of constructing such a line linking the airport with Shanganagh, near Bray, at between €7 billion and €10 billion.
Of this global figure, some €2 billion is assigned to the cost of a metro from the airport to the city centre, running via Ballymun, Finglas or Drumcondra. The city-centre stretch would be entirely underground.
Not long after assuming office last June, Mr Brennan identified an airport rail link as one of his top priorities. He even suggested that it would be in place by 2007, when the next general election is due.
Unlike the roads programme, which is financed almost entirely by Exchequer and EU funding, it is envisaged that a Dublin metro would be designed, built, financed and operated by the private sector.
This proposed public-private partnership has attracted at least 10 expressions of interest from private-sector companies, many of them international civil engineering contractors, such as Japanese conglomerate Mitsui.
It was Mitsui that first indicated its interest in the project in the mid-1990s.
Since then, a metro has formed the cornerstone of the Dublin Transportation Office's public transport plan.
As envisaged, it would run overground from Shanganagh to Ranelagh on the former Harcourt Street railway line, currently being developed in part as a Luas light rail link from Sandyford to St Stephen's Green.
Last August Mr Brennan said his intention was to abstract the proposed rail link between the airport and the city centre from this wider metro plan so that it could be delivered as a separate project by 2007.
However, a report by consultants KPMG for the RPA calculated that even a line from St Stephen's Green to the airport, which would involve tunnelling under the city centre, would take at least eight years to deliver.
Iarnród Éireann has put forward plans for a conventional rail link between Connolly Station and the airport, branching off the Sligo line, saying it could be built at a "comparatively low" capital cost of €900 million.
According to its authors, this link would utilise lightly-used sections of the network, including the old Midland Great Western line and the Newcomen Curve to gain access to Connolly and a new station at Spencer Dock.
It said a dedicated express line to the airport would be more likely to attract private-sector funding in the context of a PPP, with contributions from developers of major residential schemes planned for Pelletstown and Spencer Dock.
The rail company said its plan could be delivered within five years. However, critics have noted that much of the line would run through open countryside, doing little for public transport in Dublin.