The Houses of the Oireachtas has said it is looking at technical solutions that would allow virtual sittings of the Dáil, Seanad and committees as the Covid-19 emergency continues.
In a statement, it said this involves examining parliamentary situations in other countries to try to come to the best solution.
A Fianna Fáil member of the Dáil's Business Committee has said the Dáil meeting on a weekly basis would not be able to happen for the next four months and an alternative would have to be found.
Cork North West TD Michael Moynihan said the Dáil will have to find a way to meet remotely to discuss various issues.
He said the coronavirus has changed the world forever and "anything that was sacred six weeks ago is no longer".
Mr Moynihan said there has been a cumbersome system built around the houses of parliament and that will have to change in response to the Covid-19 pandemic.
"Inevitably the Dáil will have to find a way to meet remotely to discuss various issues, but under the rules to pass legislation we would have to be physically present, but a way around this would have to be found," he said.
Last week, the Dáil met in Leinster House despite reservations expressed by a number of TDs, including the Minister for Health Simon Harris, who said the meeting was against public health advice.
Mr Harris said with a "little bit of ingenuity" it would be possible for the Dáil to meet, citing the example of the European Parliament, which has been holding sessions via video conference.
In the UK, the House of Commons authorities announced plans to move to a virtual parliament after the Easter break if necessary.
It followed calls from across the political spectrum to set up a form of digital parliament, with proper cross-party scrutiny and debates online while MPs are unable to meet in person.
But the plans require cross-party agreement and a motion will have to be put to MPs in the parliament before it can happen.
It has been agreed here that 160 TDs will gather for a Dáil session in the Convention Centre in Dublin to elect a new taoiseach when the time comes.
The Dáil sat in Leinster House last week with a reduced number of TDs present in the chamber and this will happen again on Thursday 16 April.
But how long can TDs realistically continue to meet in person while telling the rest of the country to remain at home?
The British parliament is nearly four times the size of the Dáil and some TDs are asking if the UK can move to a virtual parliament why cannot the Houses of the Oireachtas introduce a similar system in Ireland?
The Irish Constitution was drawn up in 1937 and states that TDs must be "present and voting", so it is not clear if politicians will be able to sit remotely.
Article 15, Section 11 of the Constitution states: "All questions in each house shall, save as otherwise provided by this Constitution, be determined by a majority of the votes of the members present and voting other than the chairman or presiding members."
The Constitution also states that the Houses of the Oireachtas must sit in or near the city of Dublin or some other place where should otherwise be determined.
Fine Gael Senator Sean Kyne, who also sits on the Dáil Business Committee, said it would be difficult to hold a virtual Dáil sitting due to the rules that are in place.
"It's one thing having a virtual Dáil that is asking ministers questions but for votes it could be trickier. The Constitution states you have to be voting and present, I'm not sure how you could get around this," Mr Kyne said.
He said the plan is to hold larger Dáil sittings in the Convention Centre and also a continuation of weekly sittings with a reduced number of TDs present in Leinster House.
He said: "As long as social distancing is practiced, the numbers are reduced in the Dáil and nobody is in the chamber for longer than a two-hour period that would negate the need for a virtual Dáil."
Independent Senator and barrister Michael McDowell also said the rules set out in the Constitution would be a barrier to the Dáil sitting remotely.
He believes a designated committee should be established, which he said, could meet once a week online and put questions to ministers.
Mr McDowell said he does not believe there will be a need for many votes in the next few weeks other than on a new taoiseach.
He also said committees can operate much more effectively than the plenary sessions in the Dáil.
"You can operate committees via Zoom and there is no huge technological problem to organising a committee where 12 or 14 people could attend, and questions could be put to the minister electronically," said Mr McDowell.
Dr Jennifer Kavanagh, Law and Constitutional Electoral Law Lecturer at Waterford IT, thinks holding the Dáil in the Convention Centre is the safest way to go.
"The Convention Centre is the best way to go, they are still physically present, but they have their space," she said.
Dr Kavanagh said one of the big issues with holding the Dáil sitting digitally is the lack of reliable broadband in rural areas.
"Broadband can also be an issue in rural areas which would also pose a problem because when people are making these decisions we can't guarantee where they are all living will have reliable broadband to keep them in the room virtually," she said.
Dr Kavanagh also said it would be possible to hold committees virtually.
"The virtual option would be the way to go with committee meetings because with this it's not high stakes where votes are needed, like voting for [a] taoiseach."