A date for the vote should be known later this week
The Government has approved the draft laws they would try to bring in if the 8th amendment is repealed.
It proposes to allow abortions where a doctor assesses that a woman is not more than 12 weeks pregnant.
Seventy-two hours will have to pass between a woman seeking an abortion and it being carried out.
After the first three months of pregnancy, terminations will only be allowed where there is a fatal foetal abnormality, or a risk to the life or health of the mother.
Health Minister Simon Harris says we should know this week when polling day will be.
"This legislation is based on the policy paper which I brought to Cabinet earlier this month and is in line with the recommendations of the Joint Committee on the 8th Amendment.
"It proposes to make terminations lawful where an appropriate medical practitioner has certified that the pregnancy has not exceeded 12 weeks. 72 hours must elapse between certification and the termination being carried out.
"Beyond the first trimester, terminations will only be available in exceptional circumstances - on the grounds of risk of serious harm to the health, or life of the woman, in emergency situations or in cases of fatal foetal abnormality. In all other circumstances, abortion will remain unlawful.
"In cases where this is a risk to the life, or of serious harm to the health, of a woman, termination would not be lawful beyond viability.
"The viability of the foetus would be assessed and agreed by two doctors, one of whom would be an obstetrician/gynaecologist. If viability is established and the pregnancy is ended on health grounds then it will be done through early delivery, with a full medical team on hand.
"I also brought to Cabinet today a package of measures aimed at reducing crisis pregnancy in Ireland - including increased access to obstetric care and counselling, and contraception.
"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’s 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.
"The referendum must be passed, and the 8th amendment repealed, if anything is to change for Irish women.
"I believe that the more people reflect on the current situation in Ireland the more they will see the need for change.
"We cannot continue to ignore that fact that women are being forced abroad to have a termination, that women are purchasing abortion pills unsafely online and that women in extremely difficult situations are left isolated and neglected.
"I believe that the Irish people will vote to repeal the 8th amendment," Minister Harris said.
Meanwhile, the Tánaiste Simon Coveney has conceded his suggestion of a lock on proposed abortion laws cannot be done.
Mr Coveney had suggested the move at a Cabinet meeting earlier
A two-thirds lock would mean if the 8th amendment was repealed and new laws brought in, it would take a two-thirds majority in the Dáil and Seanad to change those laws.
Mr Coveney said it would make it impossible for one party to change the law and would stop any sliding towards an even more liberal abortion regime in the future.
It was discussed at Cabinet but it would require a change to the Constitution to do it, and Mr Coveney has conceded it is not possible in the current timeframe without greatly delaying a referendum on the 8th amendment.
Additional reporting: Jack Quann