The cabinet has received legal advice that terminations in cases of fatal foetal abnormalities would be unconstitutional.
The Sunday Business Post reports that the Attorney General told the Government that allowing an abortion in cases of fatal foetal abnormalities is 'in conflict with the Constitution'.
Legislation on the issue proposed by TD Clare Daly failed a vote in the Dail this week.
Deirdre Conroy travelled for a termination for medical reasons while she was pregnant in 2002.
She subsequently took her case to the European Court of Human Rights.
She says in cases of fatal foetal abnormalities, women should be given the choice to have a termination in Ireland