Fewer than 2,000 parents have responded to surveys on the patronage of primary schools, in a pilot scheme.
The Irish Examiner reports that only a quarter to a third of those eligible to take part in the survey have done so.
The Department of Education is seeking input from parents in Wicklow, Mayo, Waterford, Meath and Dublin, before extending the survey nationwide.
It is part of plans to divest a number of schools from the Catholic Church which governs 92% of primary schools.