The Taoiseach, Mr Ahern, is trying to reduce the time he has to spend answering questions in the Dáil, after becoming irritated at being kept in the chamber by Opposition leaders.
Since reforms in 1997 Mr Ahern has often spent six hours and more a week taking Dáil questions - far more than his European counterparts.
In contrast, the British Prime Minister, Mr Tony Blair, takes just one 30-minute session a week, and rarely appears in the House of Commons otherwise.
The Government chief whip, Mr Seamus Brennan, will tie Mr Ahern's desire to spend less time in the Dáil to the Opposition's demands for other changes when he meets the other party whips tomorrow.
Under Mr Brennan's proposals, on Tuesdays and Wednesdays Mr Ahern would take Opposition leaders' questions after the order of business.
Later in the day, he would take questions for an hour from TDs of all ranks.
However, he would not be available on Thursdays - since the Dáil's business for both Wednesday and Thursday would be rostered and agreed on Wednesday mornings.
In recent months, Fine Gael's Mr Michael Noonan, Labour's Mr Ruairí Quinn and the Greens' Mr Trevor Sargent frequently kept Mr Ahern in the Dáil for up to 90 minutes dealing with questions - to his increasing irritation.
Mr Brennan will face pressure from some of the other whips to alter the Dáil's standing rules that discriminate against Independent TDs, and those from parties with fewer than seven TDs.
Under the Oireachtas's current standing orders, 13 of the 25 Independents, Greens and Sinn Féin TDs must come together before they will be recognised as a technical group.
Independent Dublin Central TD Mr Tony Gregory has so far managed to bring 12 of the necessary 13 Independents together, including Wicklow TD Ms Mildred Fox, who supported the Government over the last five years.
Both Fine Gael and Labour say they are willing to agree on concessions for the smaller groupings - although some Government figures are privately encouraging them not to do so.
The Independent TDs are still one short of the number needed to form an official group in the Dáil, as Donegal North East TD Mr Niall Blaney has not responded to their overtures.
Mr Blaney said yesterday: "I have still not made up my mind. And I will not be doing so before Tuesday.
"No, I cannot tell you which way I am leaning at the moment."
The formation of an Independents' group would cause difficulties for both the Greens and Sinn Féin.
It would give the Independents improved speaking rights compared to both of them.
Both the Greens and Sinn Féin will push Mr Brennan to change standing orders so that they, too, are fully recognised by the Dáil.
"The rules are ludicrous," said the acting Green whip, Mr John Gormley.
Technical group status could also cause as many problems for the Independents as it would solve, since they would then be expected to spend more time in the Dáil chamber on debates.
"Is anyone seriously suggesting that some of the Independents will stay late on a Thursday to speak on the second stage of the Gas Deregulation Bill, or whatever, when they could be in their constituencies?" questioned one TD.
Besides Mr Gregory, the key figures on the Independents' side are Independent Health Alliance TD Mr Finian McGrath and Tipperary South TD Mr Seamus Healy, along with Sligo-Leitrim's Ms Marian Harkin.
Membership of a technical group does not imply agreement on policy.
It is simply a way of exercising greater influence by using Private Members' Time for priority questions to ministers.
