now understands that the watchdog is planning to ask the Department for Education to make participation mandatory for the hundreds of secondaries selected for the sample English and maths tests.
If the reforms work as planned, the NRT could provide the regulator and exam boards with the evidence they would need to allow GCSE grades to rise in future years.
But the idea of making the tests compulsory has been criticised by headteachers because it would place an extra burden on thousands of pupils as they prepare for GCSE exams. The additional tests will have to be taken by Year 11 students in March, a critical period in the revision timetable.
Brian Lightman, general secretary of the Association of School and College Leaders, said schools were already under "immense pressure" because of reforms to GCSEs and A-levels and would be "very anxious" about the new tests. He said the tests needed to be designed so that they did not "derail and upset the young people at such a crucial time in their education".
"That is what makes it very difficult," he added. "Because of the timing and the potential risks at a very pressured time for students."
Keith Grainger, headteacher of Garth Hill College, a secondary school in Berkshire, said more compulsory testing could throw GCSE plans into "disarray".
There is precedent for making sampling tests mandatory. The 2011 Education Act gave the secretary of state the power to force state schools to participate in international education surveys such as the Programme for International Student Assessment (Pisa) or the Trends in International Mathematics and Science Study (Timss).
The Conservatives said this week that they wanted additional English and maths testing of low-performing pupils in Year 7.
Russell Hobby, general secretary of the NAHT headteachers' union, said he could "see the logic" in making the NRT compulsory because he did not think many schools would volunteer.
"But that doesn't make it right," he added. "There are plenty of exams and testing going on in that period of time. It is going be very awkward for schools to then be forced to do an additional test which you cannot plan for. I don't think it would be welcomed by many schools."
Ofqual has said that 300 secondaries and around 15,000 pupils will be asked to take part in the NRT every year from 2017. Last week the regulator announced that it had selected the National Foundation for Educational Research to develop and deliver the new tests.
The regulator has said that the assessments should take less than an hour for students to complete and that the results will not be published for individual pupils or schools.
The DfE and Ofqual both declined to comment on the NRT being made compulsory.
In theory, the scheme should give hope to those who feared that, under Ofqual's "comparable outcomes" clampdown on grade inflation, GCSE results would never again be allowed to significantly improve.
But exam industry insiders worry that it will not work as intended and that Ofqual does not appreciate the technical difficulties. In February, researchers from Cambridge Assessment warned that NRT results would not be a "strong source of evidence for genuine changes in performance" in subjects other than maths and English, as the watchdog hopes.
This week Mr Hobby raised similar concerns. "It is a little bit of a stretch to say that they are genuinely able to determine improvements in the quality of teaching on the basis of performance in maths.
"It may become more of a cosmetic activity than a source of genuine information."
Ofqual missed its original deadline for awarding the NRT contract, despite extending it from August 2014 to the end of last year. TES understands that Pearson, Cambridge Assessment and Durham University's Centre for Evaluation and Monitoring all considered bidding but decided not to. Concerns were raised that the contract would "punish" a contractor that failed to set up the tests in a substantial proportion of England's secondaries in "double-quick time".
Ms Stacey has said that a small trial of the NRT will take place later this year, with another "full-cohort" trial in 2016.
`It could throw plans into disarray'
Keith Grainger, headteacher of Garth Hill College, a secondary school in Berkshire, has concerns about the details and impact of the National Reference Test.
"How will these tests sit with schools' plans for the final months of Year 11 in the preparation for GCSEs?" he asks. "It could really throw plans into disarray, especially if you aren't given that much notice.
"And what about the pupils with another test to sit when schools are already doing all they can to help them with the public exams that really matter, just a few months later?"
Nick Weller, executive principal of Dixons Academies in Bradford, is also concerned about the impact of extra tests on GCSE students. But he says that if the NRT allows Ofqual to provide "better quality assurance" and end the "volatility" of GCSE results in recent years, then it could be a good thing.