Details of a system of compensation and State assistance will be finalised at a meeting of the Cabinet tomorrow.
The women's experiences will be considered on a case by case basis by a person appointed by the State to access how best to address their individual needs.
Former residents say that a process of compensation amounting to more than €100m should be set up within a month and wound up by August, so as not to allow the issue to drag on.
Compassionate
The Government's discussion on the issue comes after a meeting in London on Saturday between a group of former Magdalene workers and Taoiseach Enda Kenny, Justice Minister Alan Shatter and Junior Minister Kathleen Lynch.
Minister Lynch said a payment is expected to be made as a compassionate gesture.
Groups representing former laundry workers have requested different compensation amounts, ranging from €60,000 to €100,000 per woman. Calls have been made for the payment of wages for the work survivors carried out at the laundries depending on their length of stay.
Taoiseach Enda Kenny is expected to make a State apology to the former Magdalene workers during a Dail debate this week, and will also outline the method of providing compensation.
Justice Minister Alan Shatter said the meeting with the 15 women in London, was "very emotional."
"This is all feeding in to what will be proposed to Cabinet on Tuesday. What we are focusing on the moment is to produce a comprehensive package of measures arising from the publication of the report," he said.
The UK-based group of former workers said it is expecting the Taoiseach to make a "wholesome" and "heartfelt" apology tomorrow.
After the two hour meeting, they said they backed a decision by the Taoiseach not to immediately apologise for the State's involvement in the institutions.
"We spoke about the apology and the women indicated very strongly about how they felt [about] obtaining an apology," said Sally Mulready, who runs the Irish Women Survivors Support Network.
"I
think there was a consensus around the room that Enda Kenny was quite
wise to have waited, to have met the women and to have read the report,
to hold the Dail debate on Tuesday," she added.
Meanwhile,
a separate group representing survivors, the Magdalene Laundry
Survivors Together Group, have also called for a national museum and
state memorial be established on the site of the last laundry on Sean
McDermott Street in Dublin.