Patient Focus, the group that represents over 100 victims of Dr Michael Neary, said it was "completely happy" with its meeting with the Tanaiste and Minister for Health today.
Speaking after the meeting, Patient Focus Chairperson Sheila O'Connor said the Tanaiste had assured them she would consult with the group before "bringing concrete proposals to Government."
Ms O'Connor didn't provide any details of any possible compensation deal. However, she said: "The proposals aren't firmed up yet but Ms Harney said she is going to come back next Tuesday or the Tuesday afterwards, very quickly, within a fortnight."
"The main thing she said was how sorry she was, and we knew she was from her demeanour and her approach. She said she wanted to sort out the issue quickly," she added.
Colm McGeehin, a solicitor for the group, said it was impossible to estimate the potential cost of compensation.
"The cost will depend on the number of people involved but it's not a huge number compared to the Hepatitis C scandal or the residential institutions," he said.
"Obviously the Minister will have to take into account that there are other people culpable here."
Earlier, the Taoiseach said compensation for the victims of Dr Michael Neary needed to be addressed, but it would not be at taxpayers' expense.
Speaking in the Dáil, Mr Ahern said the report on Neary's practices at Our Lady of Lourdes Hospital in Drogheda was damning but that its recommendations would be carefully examined and would inform legislation in the area.
The Taoiseach also apologised to Neary's victims.
"In relation to compensation, yes it is an issue that the Government will address. But the hospital is insured, the doctor is insured. We have to make sure in whatever arrangements are made, that it is not the taxpayer that picks up everything," he said.
A criminal inquiry is also expected to begin today after the National Bureau of Criminal Investigation received statements from a number of alleged victims in recent weeks.
Authorities will also be launching a probe into the whereabouts of files, relating to 44 patients, that went missing from the hospital.
The inquiry, chaired by Judge Maureen Harding Clark, found an unidentified person or persons, who had knowledge of where records were stored in the hospital, was responsible for their deliberate, careful and systematic removal.
A senior Garda source confirmed the force would be examining the report in detail and said that the possibility of a "fresh investigation involving gardaí from Drogheda and the National Bureau of Criminal Investigation on foot of the report simply cannot be ruled out at this stage".
Dr Neary, who was struck of the medical register in 2003, has suggested that someone "with an agenda to harm him" had removed the files.
The Institute of Obstetricians and Gynaecologists of the Royal College of Physicians of Ireland welcomed the publication of the Lourdes inquiry and expressed sympathy with the women affected.
The chairman of the Institute Michael O'Hare said it would be studying the content and recommendations of the report carefully.
"We will study the content and recommendations of the Report carefully and will play our full part, in co-operation with the Department of Health and Children, Health Service Executive, Medical Council and other stakeholders in ensuring that its recommendations are implemented," he said. "The public can be assured that the Institute of Obstetricians and Gynaecologists is committed to maintaining the highest standards of care in Obstetrics and Gynaecology for the women of Ireland," he added.
Speaking at the publication of a report on the practices at the Co Louth hospital, Ms Harney said an unncessary hysterectomy was a very traumatic experience for any woman.
"From their perspective this report confirms their worst fears," she said.
"I am conscious that the last few years have been particularly difficult and traumatic for many former patients of the maternity unit at Drogheda, and I want to express my deepest regret and apologise to these women and their families for what happened."