Children of four will have to sit exams within two weeks of beginning primary school, it was reported.
Tests that pupils currently take at seven to measure their level of development are to be brought forward to the start of the reception year under plans to be announced by the Government, The Times said.
The "baseline" tests are expected to be introduced in 2016 after ministers consulted on the proposals last year.
MPs are examining whether a number of different types of assessments could be approved for four-year-olds, then letting headteachers choose the one most suitable for their school.
Heads may also have the option not to enter pupils at all.
Assessments are intended to measure children's progress throughout their entire time at primary school, but having them at seven removes the motivation for teachers to push younger children to make rapid progress.
Assessing children at four raises the possibility of teachers keeping their test scores low in order to maximise pupils' improvement when they sit national curriculum exams at 11 - the progress being a key measure of a school's performance.
The plans are also likely to rouse fear in parents that tests would cause young children stress and that they may be grouped according to ability, while many experts believe that children are already subjected to too much testing in school.
According to The Times, the Department for Education (DfE) proposed in its consultation paper that the baseline assessments could involve a simple check by a teacher between two and six weeks after a child starts reception year.
Exams for 11-year-olds will also be redesigned to reflect the extra demands of the new national curriculum.
But the ranking of children according to results of new tests that would be taken at the end of primary school have been dropped after a backlash by teachers, The Times said, as have plans to tell parents how their child's score ranked on a national scale after fears it would demotivate those with low scores.