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 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."
In 2013, then-Ofsted chief Sir Michael Wilshaw slammed grammar schools, saying they "don't work" at increasing social mobility and are "stuffed full" of middle-class children. "Anyone who thinks grammar schools are going to increase social mobility needs to look at those figures," he said at the time. "I don't think they work."
A Department for Education spokeswoman said: "We don't comment on speculation."
Commenting on the reports, Dr Mary Bousted, general secretary of the Association of Teachers and Lecturers (ATL), said:
“If we are really ‘all in it together’ then the Government needs to act on child poverty, rather than tinkering with measuring it. It needs to concentrate on recruiting and retaining a qualified teacher workforce and it needs to put more funding into maintained schools, because all children have the right to a first-class education, not just those who can pay for the private tuition to get them through the 11+.
“Strikingly, even Policy Exchange says that grammar schools did not increase social mobility and out of the 164 remaining grammar schools only three have more than 10% of the pupils eligible for free school meals. And UCL Institute of Education research reveals a considerably larger gap between the wages of the highest and lowest paid individuals born in areas with a selective education system as opposed to those in an area with comprehensive schools.
“A Government which was serious about social mobility would not allow the expansion of selective education.”
Christine Blower, General Secretary of the National Union of Teachers, added: “Today’s announcement is a further step backwards for education in England. Giving the go-ahead to a so-called ‘satellite’ grammar school which is in fact 10 miles away from the existing grammar school is nothing more than a cynical sidestepping of the law which prevents new selective schools from opening.
“Proponents of selective education are curiously quiet about the impact on learners who are not selected for a grammar school education at age 10-11. For every grammar school there are three ‘secondary modern’ equivalents for those children not deemed ‘intelligent’ enough for grammar school. The NUT fears for the self-esteem of children separated from their peers at age 11.
“This new grammar schools will add to England’s already highly fragmented education system This has created an education market place where the most disadvantaged children and young people are those most likely to lose out. It is a simple fact that grammar schools have far fewer pupils with special educational needs or eligible for free school meals.
“Internationally, evidence from the OECD shows that the best performing education systems are those with ‘comprehensive’ school systems. The NUT believes firmly that the focus for an effective education service, and a more inclusive society, must be to ensure a good local school for every child and community, rather than a return to the socially divisive policies of selection.”