Action could include refusing to co-operate with the new system of assessment for three to five-year-olds, called the foundation stage profile.
Delegates at the National Union of Teachers' annual conference said that children as young as three were under too much pressure because teachers were worried about tests further up the primary school ladder.
The conference ruled out an immediate ballot but agreed to consider balloting nursery and infant teachers in September.
The decision on whether to go ahead with the ballot will be taken after a campaign this summer to enlist support from parents, governors and other interested groups.
A TES poll last week revealed that three-quarters of parents think that tests for seven-year-olds should be scrapped. However, two out of three think that 11-year-olds should be tested and even more agree with tests at 14.
The foundation stage profile is used to assess how five-year-olds perform on 13 nine-point scales. It is designed to be used for children as young as three and must be completed at the end of a child's reception year.
Members of the NUT say the tick box-style format will lead to teaching to the test in nurseries.
Judith Elderkin, head of Marlborough Road primary in Salford, said: "I fear there will be strong pressure on the most expensive private nurseries to demonstrate they are performing better than their rivals."
Alan Bradley, a Westminster delegate, said: "The downward pressure of the national curriculum is casting a grey shadow over teaching and assessment of children of five, who deserve better than this."
Supporters of the profile have said it is based on good early years practice because teachers simply have to note down observations of children over the year.
The union stopped short of calling for a boycott of tests for 11-year-olds, following its failure to win support for such action last year. Less than a third of the union's primary members voted to boycott the tests in a ballot.
Jerry Glazier, an executive member, said union members felt vulnerable in taking part in a boycott without support from members of other unions.
The Government is piloting less stressful tests for seven-year-olds in 34 authorities, where only teachers' assessment of pupils' progress in English and maths is reported.
* The Association of Teachers and Lecturers has voted to ballot for action supporting members who refuse to send national test results to the Government for use in league tables.