The Minister for Transport, Mr Brennan, will tell the Cabinet today that he favours the principle of allowing top managers at Aer Lingus to develop a bid for the State company.
However, sources said he will stress such an approach should be allowed only in the context of an open and transparent process in which rival bids would also be considered.
With political resistance building against the surprise approach last week from the airline's chief executive, Mr Willie Walsh, and two of his colleagues, Mr Brennan will brief the Cabinet today on the development.
They have sought permission to develop a bid for the airline, whose future ownership has been under Government consideration for some time.
Although Mr Walsh wants to develop a proposal before autumn, senior Government sources played down the prospects of a Cabinet decision before the summer break ends.
The Government does not want to be seen to be forced into a decision by Mr Walsh. Given the political sensitivity that surrounds a possible bid for a State asset by the public servants, it will also seek to maximise the transparency of any privatisation process.
The Government is widely expected to ask Aer Lingus directors to appoint a subcommittee of the board to oversee day-to-day control of the company by Mr Walsh in advance of any decision on ownership. Its other priority in the next three weeks will be to appoint a permanent chairman to the airline to replace the former AIB executive, Mr Tom Mulcahy, who resigned in May.
While the interim chairman, Mr John Sharman, considered the situation yesterday with the Aer Lingus company secretary, Mr Greg O'Sullivan, he is not expected to call a board meeting until after the Cabinet meets.
It is understood that Mr Brennan will outline three scenarios to the Government when it begins its consideration today of the approach from Mr Walsh.
The first option will be for the Government to do nothing to change the ownership of Aer Lingus, despite volatility in the aviation industry and the airline's requirement for up to €1 billion for investment in new fleet. The second option would allow the privatisation of a stake in the airline - through flotation or trade sale - but to exclude the airline's management from the process.
The third option would allow involvement from all interested parties, including the management.
Of those three choices, Mr Brennan is understood to favour the third. He is said to be opposed to the option of doing nothing, given the commercial pressures the airline faces. He is likely to argue that management should not be penalised by being excluded from the sale process.
He is also likely to suggest that the possible retention of a strong Irish management team to protect the airline's commitment to the domestic market.