New tests for 11-year-olds are being planned by the Specialist Schools and Academies Trust as part of a national "talent search" to help secondary schools identify their most able pupils.
It wants secondary schools to use non-verbal reasoning tests as well as data on key stage 2 test results to pinpoint the top 5 per cent pupils in England.
Professor David Jesson, the trust's associate director, said there were concerns that some pupils might slip through the net because of underperformance in the national tests.
The trust is already in talks with Government about using test data to make admissions to the National Academy for Gifted and Talented Youth more objective.
The news follows research from Professor Jesson which appeared to show a disparity in outcomes for the 5 per cent most able pupils in England, depending on whether they were in the state or private sector (see page 18).
He thinks this can be counteracted by telling schools which of their pupils fall into that top bracket so that they can help them to fulfil their potential.
KS2 national test scores would provide the basis of this. But Professor Jesson said: "There is a need to complement these tests where primary schools may have undersold children who could have performed better."
He did not want every child starting secondary school to be tested, but said there should be non-verbal reasoning tests - subsidised by the trust - that heads could turn to when they felt it appropriate.
The tests would be designed so that a pupil's performance does not depend only on language ability. Questions might include matching shapes or spotting relationships and patterns within a series of numbers.
Professor Jesson, from York university, is particularly concerned about the lack of disadvantaged children in the top 5 per cent of pupils according to national test data. He found that only 1,000, or 3.33 per cent, of the 30,000 top-performing pupils were eligible for free school meals, but he suspects the real proportion could be at least 6 per cent.
The non-verbal reasoning tests could also be used to bolster an improved admissions regime for the National Academy for Gifted and Talented Youth, he said.
At present, a letter from a teacher is judged sufficient evidence to join the academy.
Parliamentary questions show the number of academy members varied between authorities, with 1,851 from Derbyshire and none from the north London borough of Islington.
In some areas the number of academy members from independent schools is disproportionately high such as Bromley where they make up 64 per cent of the local membership.
Ken Sloan, director of corporate services at the academy, confirmed it was in talks with the trust and the Government over admissions.
From next year Mr Sloan expects schools to be told which of their pupils are in the top 5 per cent according to national test and GCSE results. They would automatically become members of the academy.