The education minister has said it would be "difficult" to facilitate pupils sitting transfer tests in their own primary schools.
Children taking the tests currently sit them in grammar schools or further education colleges.
Peter Weir said it was up to the two testing organisations and school boards of governors to decide any change.
The minister was responding to a Bangor mother who had written to him about the matter.
Naomi McBurney, who has two children currently in primary school, has started a campaign for primary seven pupils to sit the tests in the school they attend.
She wrote to Mr Weir asking for him to intervene, saying the move would minimise stress and pressure on children taking the exams.
The minister wrote back saying that while he appreciated her concern, the Department of Education (DE) had no role in the "operation, location or administration" of the tests.
"All selective schools in Northern Ireland currently utilise one or both of two privately commissioned tests, which are provided by either the Association for Quality Education (AQE) or the Post Primary Transfer Consortium (PPTC)," he wrote.
"While there is no bar on the use of primary schools for these tests, the location is a matter for the organisations setting the tests and boards of governors of the individual schools."
Mr Weir said allowing pupils to sit the transfer tests in primary schools "would require the consent of the boards of governors of all primary schools across Northern Ireland to host and facilitate the private transfer tests used by selective schools, which may be difficult to achieve".
He went on to tell Ms McBurney he would, however, like to see a more "straightforward" transfer process.
"For example, it clearly makes sense to try to avoid pupils being put through two systems, leading to five individual exams," he said.
"I understand that our selective schools are working together to examine options for a single system and this is something I hope to pursue with the schools over the coming months."
Mr Weir, however, cannot compel the two separate testing organisations to run a single test.
The PPTC and AQE have previously agreed draft plans for a common test but final agreement has not yet been reached.
There were more than 16,000 entrants for the transfer tests this year and it is estimated about 2,000 children sit both tests.