The first new grammar school in 50 years is set to be approved by Education Secretary Nicky Morgan.
She will give the green light to plans for a 450-pupil school in Sevenoaks, Kent, after months of legal wrangling, The Times reported.
Labour passed laws in 1998 banning the creation of new grammars - which are selective state schools - but existing schools are allowed to expand if there is sufficient demand.
The Sevenoaks school is not covered by the ban because it is officially an annexe of Weald of Kent Grammar School in Tonbridge.
The Department for Education said the report was "speculation" but it is understood that a written ministerial statement on school expansion will be made in the Commons.
The Times reported that Mrs Morgan will insist the decision does not mean the Government will scrap the Labour law, and the newspaper said the application would only be approved because governors met conditions set by Department for Education lawyers, including the requirement that pupils at the Sevenoaks site spend some time at Tonbridge once a week.
Campaigners in favour of more grammar schools have argued that scrapping the 11-plus test in most areas of the country has hampered social mobility for bright pupils from poor backgrounds.
London mayor Boris Johnson has described the decline of the grammar school system as a ''tragedy''.
Prime Minister David Cameron has previously said that "all good schools" should have the right to expand, including grammars, an assertion echoed by Mrs Morgan.
The expected decision was welcomed by Paul Carter, the leader of Tory-controlled Kent County Council.
He told The Times: "The school took great effort to submit their bid to give greater detailed information on how it will be one school, not two schools, and they did a very good job on that.
"The big issue about this decision is that it won't open up the floodgates. You have to have a grammar school there in the first place to expand.
"If you can't expand on-site you have to expand elsewhere, and that's all we have done in this case."
A Department for Education spokeswoman said: "We don't comment on speculation."