Samples of pupils could be tested to check standards in England rather than all seven, 11 and 14-year-olds, the head of the exams authority has said.
Progress testing methods could be brought in
Ken Boston told The Times this could be combined with progress tests for individual children, now being piloted.
The government said it did not plan to scrap national testing, adding that the regime encouraged pupils to progress.
Critics say the present system creates too much work for teachers and class work is too narrowly focused on tests.
Dr Boston, chief executive of the Qualifications and Curriculum Authority (QCA), said "finer grain" results would be achieved using the sampling technique over a number of years.
The tests are sat by all children in England at ages 11 and 14, with a combination of tests and teacher assessments at age seven.
The results of the older pupils' tests form the basis of some of the school league tables.
Dr Boston told the newspaper: "Using the same paper on a sampling basis for 10 years can give a finer-grain result than you get now.
"At the moment tests as they are should stay, but when progress tests come in, with information on pupil performance being available throughout the key stage, we could look at getting the national information in another way."
Dr Boston was due to speak publicly later as the QCA publishes its annual review - though was not expected to refer to this idea in his speech.
Similar approaches to testing are used elsewhere. Scotland, for example, now has an annual Survey of Achievement, replacing the 5-14 national tests.
A sample of pupils from primary three to S2 takes part, the results showing whether pupils are reaching expected standards for their age in literacy and numeracy.
The Scottish Executive calls it "a new, more robust system for measuring pupils' performance".
A spokesman for England's Department for Education and Skills said it was consulting on proposals for children to take more tests as soon as they were ready rather than at the end of a long key stage.
He added: "Many good schools already use optional national tests in Year 5 or enter pupils for Key Stage 3 tests a year early."
Head teachers welcomed suggestions that the national school tests for every child could be phased out, saying they had advocated this for several years.
The Association of School and College Leaders said such a system would stop teachers drilling pupils to pass the tests because the results could not be used to rank schools in league tables.
John Dunford, ASCL general secretary, said: "This method is more reliable than national tests because teachers do not teach to the test. "What we have at the moment is an indicator of how good people are at taking tests.
"And because these are high stakes tests, that can give a false picture of the real progress of the national education system."