The Primate of All-Ireland and Archbishop of Armagh, Dr Eamon Martin, has said there should be a more plural offering of schools in Ireland.
Speaking on RTÉ's Countrywide Dr Martin said it was very rare that a school will use the criterion of baptism.
"It is not even on the books for a Catholic school and I think that could easily be removed, that criterion for Baptism.
"I would not like to think that Baptism was some kind of a stamp that you had to get to get into a school" he said.
He said "alot of people on the ground" value Catholic schools and the Catholic ethos.
He said he didn't accept that all Catholic schools should be closed, but said instead things should be allowed to evolve naturally and schools should be allowed to amalgamate.
He added that there is sometimes a misunderstanding as to what Catholic schools are about and that internationally people value the Catholic school ethos.
He acknowledged that some people in Ireland would like a completely secular school with no influence of religion, adding "I sometimes wonder is that not in itself an ideology." He said he hopes the Irish education system can evolve in a calm way.
He said in his 28 years of priesthood he has never encountered parents who he sensed were baptising their child in order to make them eligible for a certain school.
Referring to the passing of the same-sex marriage referendum last year he said "I still believe marriage is between a man and a woman. I also respect the fact that there are many families that don't live fully in accordance with the Catholic church".
He said it is important that the church is given the space to explain its point and others are allowed to share their views.
Referring to people in favour of same-sex marriage he said "these people are still wanted as part of the Christian family and Catholic family."
He said he was hopeful Pope Francis would come to Ireland for the Catholic World Meeting of Families for 2018.