Ministers are planning to revive national tests for seven-year-olds in England, according to the Times Educational Supplement.
Currently, Year 2 pupils sit tests in reading, writing, maths and science which are marked by teachers and moderated by local councils.
The results of any new tests would be used to hold schools to account on pupils' progress, the TES says.
Teaching unions have already threatened to boycott any new national tests.
Schools Minister Nick Gibb is reported to be considering the proposals as his department gets to grips with how pupil progress is to be measured and recorded now the system of National Curriculum levels has been scrapped.
This was the system of checking pupils' year-by-year progress against a set of national expectations.
'Step too far'
Pupils are expected to reach two levels of progress between the end of infant school - or Key Stage 1 (KS1) - and the end of primary school, or Key Stage 2 (KS2). Schools are held to account on this through the league tables.
A source told the TES: "Nick Gibb is looking at the idea of scrapping teacher assessment in KS1 tests entirely in favour of having reported tests.
"It is because there is a difficulty with using teacher assessment for progress, plus they want to reduce teachers' workload.
"The issue is that you can't measure progress accurately with teacher assessment, and there are incentives for schools to depress pupils' scores to show progress is being made."
Any move to bring in national tests for infant pupils would be controversial, as teaching unions have long argued that they skew learning and can set children up to fail in the early years, when youngsters develop at different speeds.
The KS1 national tests for seven-year-olds were scrapped more than a decade ago after complaints that seven, or six in some cases, was too early an age to put children through the stress of external testing.
Russell Hobby, general secretary of the National Association of Head Teachers, which represents mainly primary schools, said reintroducing these tests would be seen as "a step too far".
He added: "My members would take it very badly if they had to abandon teachers' assessment, which was a key part of the review we agreed upon years ago."
Mary Bousted, general secretary of the Association of Teachers and Lecturers, said bringing back tests would be a "total nonsense".
However, the move is supported by Ofsted chief inspector Sir Michael Wilshaw, who, in 2013, called for the return of the tests.
Formal, externally marked national tests for 11-year-olds remain and are used to measure how well schools are serving pupils through school league tables.
A Department for Education spokesman said: "Tests have always been a part of assessment arrangements at Key Stage 1.
"We have already announced that tests to assess the new national curriculum are being developed, to be brought in from summer 2016, and schools will be informed of the arrangements for teacher assessment by September 2015."