Taoiseach Micheal Martin is to brief party leaders on Friday about the controversy surrounding Supreme Court judge Seamus Woulfe.
Mr Martin said the meeting is to collectively agree how to deal with the issue.
The Irish Government earlier this week received legal advice after the Chief Justice said the judge should resign over his attendance at the controversial golf-gate dinner in Galway.
The Government reviewed the correspondence between Mr Justice Frank Clarke and Mr Justice Woulfe, which was published on Monday.
During a meeting the Chief Justice told the judge he should resign, a position he then repeated in correspondence between them.
The Ceann Comhairle Sean O Fearghail warned TDs about making any comments about the controversy, over concerns it could be viewed as bias.
Mr Martin told the Dail that he wants to see a consensus among parties on how to deal with the issue.
Attorney General Paul Gallagher outlined "serious constitutional issues" arising out of the controversy, to Cabinet members.
Article 35.4 of the Constitution of Ireland says that a judge of the Supreme Court or the High Court shall not be removed from office except for "stated misbehaviour" or incapacity, and only upon resolutions passed by the Dail and by the Seanad calling for his removal.
However the Article does not set out the process by which the Oireachtas can pass the resolution.
Mr Justice Woulfe, a former attorney general who was appointed a judge of the Supreme Court in July, faced criticism after it emerged he was among 81 guests who attended the Oireachtas Golf Society dinner in August.
The chief justice met Mr Justice Woulfe last week as part of a resolution process emanating from a report investigating Mr Justice Woulfe's decision to attend the golf event amid coronavirus guidance against large indoor gatherings.
In a letter to Mr Justice Woulfe, Mr Justice Clarke outlined his concerns over how the judge has handled the incident.
Sinn Fein president Mary Lou McDonald said she hopes party leaders will be "fully and properly briefed".
"I will go on in with a ready ear and an open mind," she told the Today With Claire Byrne show.
"I want to hear what the Government has to say and importantly what the attorney general has to say."
Ms McDonald repeated the party's position that Mr Justice Woulfe's position is "untenable".
"The publicly known facts are that the chief justice has suggested by letter that Justice Woulfe should resign," Ms McDonald added.
"I think that creates clearly a problem and clearly an issue around tenability of Justice Woulfe's position.
"I think where the chief justice has lost confidence then yes, I would have thought that is manifestly the case.
"The issue now, it seems to me, is how do you, within the rules and respecting and recognising the divisions of powers, navigate that.
"How did this all happen, how did we land in a mess like this?
"I will go to the briefing today with an open ear and listen to how we got to this point and listen to what the attorney general and Government are saying."
