The issue of the 11-Plus has proved controversial
A new post-primary transfer test for schoolchildren in NI would be a "climbdown", according to the SDLP.
Education Minister Caitriona Ruane will reveal her plans on Thursday.
She is to propose a form of testing to continue for three years, but there will be a limit on the number of pupils grammar schools can take on that basis.
Dominic Bradley, SDLP, said it had the hallmarks of a DUP/Sinn Féin deal. But Sinn Féin's John O'Dowd said Ms Ruane was setting out a clear way forward.
Last December, Ms Ruane announced that the test, commonly known as the 11-plus, would come to an end in 2008.
It is believed that now, the minister could commission new tests which encompass broader educational areas than the current transfer test.
These tests would be developed and marked by the Council for the Curriculum, Examinations and Assessment, continuing for about three more years.
Education Minister Caitriona Ruane is to reveal her plans on Thursday
Mr Bradley said if the reports were true, Ms Ruane had made a "mockery of Martin McGuinness's assertion that he had ended the 11-Plus".
"This is clearly a climb-down from the minister's stated position on academic selection and has all the hallmarks of a hastily cobbled together deal by the DUP/Sinn Fein government," he said.
"The minister has caved into pressure from those who are opposed to reform.
"This decision is the thin end of the wedge for the continuation of the 11-Plus into the future and is an indication of the minister's failure to carry through reform."
However, Mr O'Dowd said the education minister was setting out clear proposals about how children would transfer from primary school.
"She has also set out a clear way forward that allows those current grammar schools who request to do so a 'transitional' period, ending in 2013, to have a limited percentage of academic admission - this is designed to ensure smooth transition for children," he said.
"The majority of children from 2010 will transfer to their post-primary school on the basis of non-academic criteria at 11 and make the important decisions about their futures on the basis of informed choice at 14.
"Academic selection has no place in a modern education system from 2013 all academic selection will end.
"I would urge everyone to read the full document carefully and for those who are opposed to academic selection to make their view heard as the pro-grammar lobby will clearly attempt to undermine the ending of academic selection and cause further confusion to parents and pupils."
Sir Kenneth Bloomfield from the Association for Quality Education said a definite decision needed to be made.