Members of the three Government parties are now likely to be given a free vote on a bill to allow for assisted dying.
The Dignity in Dying Bill is to be debated by TDs next week after it was selected from the lottery at the Dáil business committee.
It is understood that the majority of TDs in Fine Gael, Fianna Fáil, and the Green Party would like to be offered a free vote on the matter.
Labour, Sinn Féin, and the Social Democrats have come out in support of the bill, which has been put forward by People Before Profit TD Gino Kenny.
When asked if a free vote would be given to the Government parties, Green Party leader Eamon Ryan told the Dáil the legislation has not yet been discussed by Cabinet or by his party.
But he added: "My understanding, and certainly with my party, is that such flexibility or such an approach is a real possibility. It is not the norm in this House, but where there are matters of complex conscience and very different views, that tends to be a possibility. I certainly would not rule it out."
He added that the issue is "not something on which we would divide on party-political grounds".
There was broad agreement at a meeting of the Fine Gael parliamentary party this week that members should be allowed to vote as they wish on the matter.
Tánaiste Leo Varadkar told party colleagues that he favours the establishment of an all-party Oireachtas committee to look into the issue of assisted dying.
Justice minister Helen McEntee put forward a number of options at the meeting, including holding a citizens' assembly on the issue.
However, most members of the party, including Mr Varadkar, voiced support for an Oireachtas committee, similar to the one that was set up around the eighth amendment.
Fianna Fáil has yet to discuss the issue, but sources said that a vote of conscience is likely to be given to members.
Mr Kenny said it is now imperative that the bill progresses to committee stage, if voted for by a majority of TDs next week.
"This bill is a very important piece of legislation that is necessary to give to a person the legal and medical right of the authorisation of assisted dying where that person is suffering from a terminal illness," he said.
"It is to provide choice for people who have been given a terminal diagnosis — a choice to end their life in a dignified way, and on their terms."