Liberal Democrats have vowed to fight any attempt to open new grammar schools, amid growing speculation that Prime Minister Theresa May might be preparing to lift the ban on their creation.
The Sunday Telegraph reported that the PM could announce a new wave of selective schools as early as the October Conservative conference.
The paper quoted an unnamed Government source as saying that allowing new grammars would be about "social mobility and making sure that people have the opportunity to capitalise on all of their talents".
But Downing Street sources pointed to Education Secretary Justine Greening's comments last month that the issue was in her "in-tray" and she would take time to consider it before any announcement is made.
Ms Greening said at the time she was "prepared to be open-minded" about school selection, but signalled that this might not mean a return to the old pattern of grammars and secondary moderns by stressing that education was no longer a "binary" world and that there were already a range of different types of school on offer.
Mrs May is thought to be a supporter of new selective schools having backed a grammar school's proposal to open a new "annexe" in her Maidenhead constituency.
And the PM's new chief of staff Nick Timothy has also backed new selective schools in the past.
Mrs May's predecessor David Cameron annoyed some Conservatives backbenchers by resisting the creation of new grammar schools.
Responding to the Sunday Telegraph report, Liberal Democrat leader Tim Farron said: "Lib Dems will work to block any Tory attempt to create grammar schools."
Labour's former shadow education secretary Lucy Powell said reintroducing grammar schools across England would be an "incredibly backward step".
"All the evidence tells us that, far from giving working class kids chances, they entrench advantage and have become the preserve of the privately-tutored.
"The particularly startling aspect of this development is that the new Education Secretary is considering allowing existing free schools and academies to adopt selective admissions."