The Government Chief Whip Mary Butler will table a proposal on Thursday to try to resolve the dispute over the allotted Dáil speaking time for Regional Independents, which delayed the nomination of the Taoiseach last week.
This afternoon the Dáil Reform Committee held an online meeting to discuss the contentious issue, and it will hear legal advice on the matter on Wednesday.
Independent TDs who support the coalition might be given Government speaking time to raise issues during Leaders' Questions.
Leaders' Questions is the key part of the Dáil schedule on Tuesday and Wednesday, where opposition leaders pose queries to the Taoiseach.
The same applies on Thursday when the Tánaiste answers questions.
Now in what would be a major change of the rules, TDs backing the Government could get their own slot to raise issues during this allotted question time.
Some of those attending the meeting today said a similar system in the UK during Prime Minister's Questions in the House of Commons.
Should it be accepted, the change has the potential to diffuse the bitter political row over the Regional Independents' bid to speak from the opposition benches.
This evening, the opposition appear to be reserving judgement until the Chief Whip's proposal is presented on Thursday.
However, Social Democrats Deputy Leader Cian O'Callaghan said it became clear at today's meeting that government parties are attempting to mount a rearguard action to reduce Opposition speaking time and designate it for the government and he said this will not be entertained.
"There is another way. To help resolve the dispute over speaking rights, and the instability that pandering to Mr Lowry is causing, the Government must cut all ties with him.
"This means ending all preferential treatment, briefings, informal deals and arrangements that have been made with Mr Lowry in return for his support." he said.
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