Pilots of the tests, also known as "single-level", are taking place in more than 400 schools. They have confirmed experts' warnings that it is difficult to design a test for a single national curriculum level appropriate to pupils of different ages.
The key stage 2 exams, for example, could see children ranging in age from eight to 12 being tested on the same material.
One alternative that has been considered is setting several different tests for the same level, with each suitable to a different age group. But ministers fear this could create problems for the qualifications regulator, Ofqual, in checking that all tests for the same level are of the same standard.
The single-level tests were being designed as a more flexible replacement for the current national testing system, which has a question mark over its future following the summer's marking shambles.
Ministers have expressed hope that the problem can be ironed out and the tests introduced nationally as early as 2010, The TES understands.
But last week Jon Coles, acting director-general for schools at the Department for Children, Schools and Families, suggested this was unlikely. "The expectation might be that there will be some more years of the key stage 3 tests," he told a school improvement conference in Northampton.
Lord Adonis, the former junior schools minister who moved to transport this week, also gave strong hints about problems over the introduction of single-level tests during a meeting with headteachers in London last month.
A source who was present said: "There is nervousness about taking the national tests away without having a ready substitute. He was giving heavy hints that Sats were here to stay."
Government sources say the pilots have shown schools are receptive to the idea of taking tests when they feel pupils are ready because there is less pressure involved.