Steven O'Riordan, head of Magdalene Survivors Together, said the women he has worked with are happy to meet Enda Kenny and Eamon Gilmore "any time, anywhere".
"The women believe it's significantly important that they meet directly with the Taoiseach. They feel that by relaying their stories personally he will recognise the importance of giving a full apology," he said.
"I am optimistic a state apology will come in two weeks. I think he will do the right thing."
Survivors of the laundries have criticised the Government's response after a report showed a quarter of the 10,000-plus women detained in the slave-like regime were sent by state authorities.
The group requested a meeting with the Taoiseach after the report was published on Wednesday.
Meanwhile, advocacy group Justice For Magdalenes, which has been fighting for a state apology, has warned the Government that many survivors will only meet the Taoiseach and Tanaiste if they are assured of confidentiality.
The advocacy group said talks would be a huge step forward but only if privacy was a guarantee.
Katherine O'Donnell, University College Dublin researcher and member of the Justice For Magdalenes group, said many women would only agree to the meeting if they could be assured of privacy.
"The women we are in touch with, none of them would want to be publicly identified. Maybe that would change if they were told what happened to them was wrong," she said.
"We won't be bringing any women to a publicly known meeting. There are women who are brave and able to be publicly identified with their Magdalene past and we applaud their bravery. If a meeting does take place with them, that would be wonderful but it would only be a tiny step forward."
Mr Kenny was accused of a "cop-out" following the report's publication when he said he was sorry for the stigma attached to the women, but stopped short of issuing a full apology on behalf of the state.
He has appealed for time to consider the report in full.
Ms O'Donnell is running a UCD project in the women's studies centre in the School of Social Justice to record oral accounts of Magdalene survivors, relatives, members of the religious orders and anyone who wishes to share memories and experiences of the institutions.