Education Secretary Justine Greening has said the Government's proposal to ask companies to reveal the numbers of foreign workers they employ will not be made public.
The idea - announced by Home Secretary Amber Rudd during last week's Conservative Party Conference - had faced a growing backlash, with business leaders describing it as divisive and damaging.
Speaking on Peston on Sunday, Ms Greening said the statistics would be used to identify which sectors and areas of the country were facing a shortage of British workers.
Ms Greening added that she did not believe Ms Rudd said the results would be published.
The Putney MP also confirmed that foreign academics would be allowed to advise on Brexit, and that this had never been stopped.
Also on the subject of Brexit, Ms Greening said that nothing was "off the table" and the Government would respond to people's concerns on immigration, but make sure Britain could still trade effectively.
On the subject of grammar schools the Education Secretary refused to suggest how many schools might be built, saying that it was up to local communities to make that decision.
She also said if grammar schools were built, the country would not return to a binary system of education and that tests would be created in such a way that children could not be tutored for them.
Ms Greening opposes a third runway at Heathrow Airport and when asked if she would resign from her position if the plans were approved, she answered that she would not answer "hypothetical questions about decisions which have not been taken".