More than one thousand couples have been referred for free fertility treatment since the scheme was introduced last September.
The first baby conceived through the programme has been born, according to the Health Minister.
Stephen Donnelly told The Journal that he wants to expand the eligibility criteria.
Dr. John Waterstone from the Waterstone Clinic in Cork says there are a number of restrictions, including a maximum age of 40 for mums, and couples have to be in a relationship for at least a year:
"Treatments involving donor eggs and donor sperm so far has not been funded which obviously excludes same sex female couples who need donor sperm to have a baby and also it excludes single women who are wishing to alone and have a baby using donor sperm."
