A boycott of national tests would cause a "great deal of frustration" for governors managing the fallout in schools, the chair of the National Governors' Association has said.
Clare Collins spoke as teaching unions the NUT and the NAHT confirmed this week that they would go ahead with a ballot of members in the run-up to the tests in May.
Ms Collins said the association was lining up its lawyers to look at the legal implications if the unions decide to boycott the tests.
It has not yet been confirmed when the ballot papers will go out, but it is understood the vote will take place as close as possible to the start of the Year 6 Sats in the second week of May.
The Government has already claimed that for headteachers to refuse to go ahead with the tests would be "unlawful", although the unions have said the boycott would count as a trade dispute.
Unions are not allowed to carry out industrial action for "political reasons" but they can for any issues relating to pay and conditions.
This week, both unions claimed the tests caused unnecessary stress.
Ms Collins said that in the event of a boycott, governors in schools where opinion is divided might feel under pressure to help in administering the tests. "We will be advising them not to do that," she said.
She added that governors could be put in "an extremely difficult position" in dealing with their heads.
"If someone doesn't fulfil their contractual obligations, it's a legal issue," she said.
She said the association would prepare official guidance to governing bodies only if the unions confirm they are definitely going ahead with a boycott.
In this week's announcement, both the NAHT and the NUT stressed that any boycott "would categorically not be strike action".
The aim, they said, would be to "frustrate" the administration of Sats, and pupils would attend school as normal instead.
They also pledged to give the parents an "absolute guarantee" of their child's progress at the end of their primary years.
Christine Blower, general secretary of the NUT, said the lack of response from the Government on the issue had been "disappointing".
"We want to avoid industrial action and call upon the Government, even at this late stage, to enter into meaningful talks," she said.
Mick Brookes, general secretary of the NAHT, added that his association had put forward a "viable and professional alternative" to Sats testing.
Vernon Coaker, schools minister, said considerable progress had been made in strengthening the role of teacher assessment, but added that it was "time to challenge the myth that children spend their entire primary school career preparing for the tests".