Senior Ministers are believed to be divided over whether the Dublin Airport Authority (DAA) should be allowed take part in a tender process to select the operator of the new terminal at the airport.
While agreement over who builds the facility is believed to be possible, there is no agreement this weekend on whether the DAA should be allowed to become the operator as well.
The Cabinet is likely to discuss the issue on Tuesday, although a decision could once again be deferred. Expectations are growing that a third terminal may also be proposed by the Government.
This facility would not be built for many years, but might come onstream if passenger numbers threatened to overwhelm the second terminal.
The most likely site for a third terminal would be to the west of the airport. The major landowners in this area are the businessmen Ulick and Desmond McEvaddy.
They have previously signalled that, while they would like to develop a terminal immediately, they would support the idea of building on the west side some years down the line.
While political differences continue on the terminal issue, at this point agreement is in place to sell over 50 per cent of Aer Lingus, with consultants likely to be appointed to advise on the best method of selling the equity and the best time to do it.
The airline's new chief executive, Dermot Mannion, does not take up his job until August.
While the Government remains concerned about landing slots, there is widespread agreement that selling off part of the airline is the only way Aer Lingus can secure funding for its ageing long-haul fleet.
An alternative proposal suggested by ICTU general secretary David Begg for a State holding company has not found support at a senior Government level so far.
Mr Begg believes pension funds could invest in the State holding company and this would free up capital for Aer Lingus. This week, Mr Begg wrote to the Government asking for some kind of response to the ICTU proposals.
Political sources have indicated the DAA would like to own, build and operate the facility, but the Tánaiste Mary Harney remains steadfastly opposed to this idea. However, some Ministers argue that it would be pointless, and possibly unlawful, to exclude the DAA from any EU-wide tender process.
The DAA chairman, Gary McGann, has said the authority is "ready, willing and able" to build a new terminal, although he believes airport charges will need to rise significantly to fund the development.
Meanwhile, in Cork yesterday, Transport Minister Martin Cullen said he was not prepared to make a decision yet on whether Cork airport should accept €160 million of debt associated with the new terminal at the airport. He refused to comment on whether the debt should go on the balance sheets of Cork or Dublin airport.
Additionally, he said he wanted to see the business plans of all three airports before making any decision.