Theresa May is planning to end the ban on new grammar schools in the latest mark of her rein as Prime Minister.
The Conservative leader is looking at abandoning the ban that was imposed on selective schools nearly 20 years ago by Tony Blair in 1998, a change opposed by opposition parties.
Labour leadership contender Owen Smith said grammar schools entrench disadvantage and "don't overturn it". He pledged "fight tooth and nail" against any plans lifting the ban.
The decision is expected to be announced at the end of the year, and possibly as early as October, at the Conservative party conference, the Telegraph reported.
While Tory backbenchers have pushed for grammar schools, David Cameron stood firm on the issue.
Chair of the Conservative backbench 1992 Committee Graham Brady told the Telegraph that the change would help "raise standards in state education".
"The ban on new grammar schools introduced by Labour makes no sense and is an unjustified restriction of choice for parents and communities that want this kind of education."
Education secretary Justine Greening said in July that she was open to the possibility of allowing new grammar schools.
However, Labour hit back at the policy. Shadow education secretary Angela Rayner said: "Rather than harking back to a mythical ‘golden age’ of grammar schools, the Tories must work tirelessly to improve every school in the country, to work with teachers to drive up standards, and to give our schools the investment they need in the 21st Century.
"Selection belongs in the dustbin of history and has no place in modern society. There must be no going back."
Liberal Democrat leader Tim Farron said: “Lib Dems will work to block any Tory attempt to create grammar schools.”
The move also signals the latest bold move by May. Earlier this month she made a major restructure of government, bringing together two substantial departments to create the single office for Business, Energy and Industrial Strategy.