First Minister Arlene Foster has vowed she will work to ensure one single agreed transfer test for 11-year-olds.
For the past number of years, Primary 7 children have been faced with two separate sets of unofficial transfer tests to be considered for entrance to most grammar schools in Northern Ireland.
The AQE system is used mostly by controlled and voluntary grammars, and the GL Assessment system is used mostly by schools in the Catholic sector.
And 2015-16 is the seventh year that the unofficial transfer tests have been run.
More than 14,500 children sat the unofficial transfer tests last year - 7,700 sitting the AQE test, and 6,803 taking the GL tests.
The unofficial tests were established after the official 11-plus transfer test was abolished in 2008, at a time when Sinn Fein veteran Martin McGuinness - now Deputy First Minister - was in charge of the Department for Education.
The DUP nominated an Education Minister for the first time last week. Sinn Fein had been the only party to hold the portfolio since the reintroduction of devolution to Northern Ireland
New Education Minister Peter Weir MLA said last week that he is convinced that a single 11-plus-style test is "worth exploring".
And last night, First Minister and DUP leader Arlene Foster told the BBC that she felt change was possible.
"People have felt that because there are two tests that it can be quite pressurised for children when they are taking those tests," she told the BBC's Inside Politics programme. "Children have to take tests over a long period of time.
"We will look at that, we will talk to the people involved, we will see if that can be done for this year.
"It's something that I think can be done."
In January this year, the First Minister - herself a product of a grammar school education - said that her priorities in the field of education were ensuring every young boy and girl had an opportunity for a good education - and to establish one single transfer test for primary school pupils in Northern Ireland.