The plan by a group of 15 current and former grammar school principals was revealed on Wednesday.
Bishop of Derry Donal The Most Reverend McKeown said it appeared to be “setting in concrete the fragmentation” of decision-making in the North of Ireland’s education system.
He questioned if it was appropriate for principals to be making the proposal.
Speaking to BBC News NI’s Good Morning Ulster programme, he said: “This really is a challenge for our politicians to say: ‘Who runs the education system?'”
Grammar school principals were consulted on the plans during the summer and they were sent to boards of governors in early September.
Governors have been asked to decide whether to sign their schools up to the plan by 3 pm on Wedenesday, September 29.
It is understood that the majority of grammar schools have already agreed to the plans but a minority remain opposed.
If confirmed, the plan for the single common transfer test would bring to an end the existing system of separate tests run by the Association for Quality Education (AQE) and the Post Primary Transfer Consortium Ltd (PPTC).
None of the group of principals behind the common test proposals agreed to be interviewed by BBC News NI.
Bishop McKeown said: “We have a desire for greater integration across our education system and this actually seems to be setting in concrete the fragmentation as to who decides about the outcomes for the education system.”
The Catholic Church opposes academic selection in Northern Ireland but Catholic grammar schools continue to use the transfer test system.
Bishop McKeown said schools should focus on ensuring “quality outcomes for all young people”.
He described the transfer test as a “fake exam which claims to measure intelligence but really is only a competition for those who are best prepared”.
“Unlike most other countries we think we have to have grammar schools, which are for good pupils, and the rest of the schools for everybody else,” he said.
“That seems to be a system that every other country has left behind.”
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