A number of legal experts have said there is no constitutional barrier to allowing equal access to Catholic schools if children are not baptised.
The Taoiseach has said there could be legal challenges to changing admissions policies.
However research by charity Equate, which is campaigning for an end to the "baptism rule" in Catholic schools, found this may not be the case.
Equate said the opinion from three constitutional experts said that there is no constitutional barrier to amending the Equal Status Act removing the baptism barrier.
The advice was drafted by Dr David Kenny of Trinity College, Dublin, Dr Conor O'Mahony of University College Cork and Dr Eoin Daly of NUI Galway.
Labour's education spokesperson Joan Burton said religious values were a matter for individual schools, but entry should not be based on it.
"We have practice on the ground in Ireland which can be quite good but in others cases, there have been cases of discrimination and we want to take that out of the law," she said.
Ms Burton told Newstalk Breakfast today that she will present a Private Member’s Bill in the Dáil next week seeking an amendment to the Equal Status Act to allow equal access to Catholic schools, irrespective of religion and whether or not a child is baptised.