Almost 2,000 parents have participated in a Department of Education survey to measure demand for new kinds of primary schools in five towns and areas around the country.
The survey, of parents of primary and pre-school children, closed on Friday.
The areas were Arklow, Castlebar, Tramore, Trim and Whitehall. A total of almost 10,000 children attend primary schools in these five places.
The initial data does not identify whether respondents were the parents of primary or pre-school children.
More than 90% of primary schools are currently run by the Catholic church.
The department says the information gathered will allow it to identify the level of parental demand for a wider diversity of school choice.
Where such demand is identified, it says the options for a possible transfer of school ownership of some schools will be considered.
An additional 39 areas will be surveyed shortly.
Both the department and Minister for Education Ruairi Quinn say they are satisfied with what they call an "encouraging" level of interest from parents in the five areas.