Independent TD Finian McGrath is planning to reveal in the Dáil this week details of his agreement with the Taoiseach in return for supporting the Government.
Mr McGrath told The Irish Timeslast night that he hoped to read at least part of his agreement into the record of the House today or tomorrow.
This will include "clarification" of the commitments he got from Mr Ahern on the use of Shannon airport by US military.
He said part of his agreement with Mr Ahern was that he would get a certain amount of Government time to address the Dáil, and he was to meet with the chief whip, Tom Kitt, to discuss that today.
"I am not sure, therefore, what day I will have time to speak in the Dáil this week, but I do hope to get some of what I agreed with the Taoiseach out there".
Mr Kitt said last night that standing orders would not be changed to allow speaking time for the four Sinn Féin deputies and Independent Tony Gregory.
Under current rules a "technical group" of seven or more Opposition TDs can be formed to access speaking rights. With four of the Independents supporting the Government, there are not enough TDs to make up seven.
Mr Kitt said the electorate had decided, the figures did not add up and there would be no changes.
Sinn Féin is holding a protest at the gates of Leinster House today to highlight what it says is an attempt to "gag" its TDs.
The Dáil will resume today for the first time since the election of Taoiseach, and will sit for the next two weeks before the summer recess.
The main business this week will be the Government's legislation to abolish stamp duty for all first-time buyers and which the Green Party will support.
Under the Finance Bill Number 2 Act, all first-time buyers will be exempt from stamp duty irrespective of the cost of their house, backdated to March 31st.
The Ministers and Secretaries (Ministers of State) Bill 2007, to allow for an increase in the number of junior ministers, will also be before the Dáil this week.
Meanwhile, the Labour Party will today vote for party frontbench spokesman Brendan Howlin when he is proposed as leas ceann comhairle.
Mr Howlin told a recent Labour Party parliamentary party meeting about an approach from the Taoiseach to him about the position.