The Cabinet has approved the draft laws they would try to bring in if the Eighth Amendment is repealed.
It proposes to allow abortions where a doctor assesses that a woman is not more than 12 weeks pregnant.
72 hours will have to pass between a woman seeking an abortion and the termination being carried out.
After the first three months of pregnancy, terminations will only be allowed in limited circumstances - where there is a fatal foetal abnormality, or a risk to the life or health of the mother.
A debate on holding the referendum has just started in the Seanad, and Health Minister Simon Harris says we should know this week when polling day will be.
He said: "Earlier this year I set out a very detailed, ambitious and demanding timetable to facilitate a referendum by the end of May and I'm pleased to say that it is firmly on track.
"I expect that we will be in a position to set the polling day this week so that the people of Ireland will know exactly what day in May this referendum will take place."
Simon Coveney's plan for a two-thirds majority lock on new abortion laws is unconstitutional, according to opposition TDs.
The Tánaiste's proposal would mean two-thirds of the Dáil and Seanad would need to approve any further changes to abortion legislation.
The plan is part of a bid to stop any further sliding towards more liberal laws, if the government's current plans get approval.
The Iona Institute, Labour leader Brendan Howlin and Social Democrats TD Catherine Murphy have criticised the idea, saying that it would be unconstitutional.
Speaking to RTÉ’s Morning Ireland, Deputy Howlin said: “I have no doubt that what he is suggesting is unconstitutional.
“The problem is if that was inserted in the law, prima facie, that law would not be constitutional itself and I wouldn’t want to put the really hard work of advancing this case at risk.”
Deputy Murphy echoed his sentiments, saying: "Each vote is of equal value, and I think what he is proposing, if you were to take it to a logical conclusion would actually require another amendment to the Constitution.
"So I think he's got to really rethink that."
The Constitution says that all votes in each house of the Oireachtas shall be determined by a simple majority of voters present, unless there is an article in the constitution saying otherwise.
Health Minister Simon Harris has said he is open to considering the idea, however.
Health Minister Simon Harris has said that says he expects the Government to set a date for the referendum on the 8th Amendment this week.
Cabinet is today discussing the proposed legislation that would be introduced if the 8th Amendment is repealed.
It includes allowing abortions to be carried out by medical practitioners through abortion pills up to 12 weeks, a three day cooling off period and restrictions on late-term abortions.
Minister Harris said that he is aiming to announce a May date for the referendum this week, so people can plan to be in the country.
"I look forward to a detailed conversation today in relation to the legislation, but not just that, also in relation to a range of measures we can put in place to reduce crisis pregnancies in Ireland," he said.
"This is a significant day, the Cabinet will consider this issue today, I'll take the Referendum Bill into the Seanad tonight and tomorrow.
"Subject to the Seanad passing this Bill this week, we will set the polling day for the referendum on the 8th Amendment this week."
The Tánaiste wants proposed new abortion legislation to include a two-thirds majority lock to prevent it being easily changed in the future.
It would mean any alterations to abortion laws in the future would need the support of two-thirds of the Dáil and Seanad.
Cabinet ministers will discuss the general scheme for what abortion laws they would aim to bring in if the 8th amendment is repealed this morning.
After declaring he has changed his mind on the issue yesterday, Simon Coveney will tell his colleagues there needs to be more protection to prevent any laws being changed easily in the future.
He will say a two-thirds lock system would make it impossible for any one political grouping to change the law.
It is seen as a counter move to those on the pro-life side claiming these proposed new laws would open the floodgates for abortion on demand, and avoid any creeping change on the issue.
A two-thirds majority would be more than Fine Gael and Fianna Fáil combined in the current Dáil.
What Ministers are considering this morning proposes allowing abortions to be carried out by medical practitioners through abortion pills up to 12 weeks gestation.
A three-day cooling-off period will be required from when a woman seeks an abortion to when she gets the pill.
There will also be restrictions on late-term abortions in the cases of fatal foetal abnormality or risk to the life or health of the mother.
The Save the 8th campaign has criticised Minister Coveney’s proposals, saying they are "crazy, unconstitutional, and telling".
Save the 8th’s Niamh UiBhrian said: “We agree with Simon Coveney that politicians simply cannot be trusted with abortion, and that additional safeguards are needed. But what the Minister is proposing is crazy, unconstitutional, and telling. Article 15 of the constitution says that all matters before the Dáil shall be decided by simple majority.
"It is absolutely astonishing and outrageous for the second most senior figure in the Government to effectively mislead the public about what can be included in a contentious piece of legislation.
She added: "If the Tánaiste genuinely wants additional protection for the unborn, he needs a constitutional amendment – but he is campaigning to get rid of just that.
"What the Tánaiste is saying this morning is that he does not trust politicians to legislate on abortion. He is not alone.”