INTO general secretary John Carr described Bishop O'Reilly's comments as "significant".
But the union insisted there would have to be dialogue on the subject before they could give it their backing.
The move is set against a backdrop of huge changes in the primary education landscape and the prominent role traditionally held by the Catholic Church, which is patron of over 90pc of the nation's 3,300 primary schools.
Outlining a vision for life in Catholic primary schools, Bishop O'Reilly said Catholic education was rooted in faith.
He said faith could not be compartmentalised and that religious education was a priority in a Catholic school and required a serious commitment of time and resources.
"Teachers teach by example as much as by words -- their Christian witness, the values and attitudes that they embody in their daily interaction with those around them," he told the annual conference of the Catholic Primary School Manager's Association (CPSMA).
"We also need to encourage teachers who are capable of exercising leadership in schools to do post-graduate qualifications in Catholic school leadership," Bishop O'Reilly added.
"I believe we need to be prepared for the day when such qualifications will not be just desirable in candidates for leadership positions, but will be a requirement."
Mr Carr said the remarks must be seen in the context of current lack of supports for school leadership.
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