The move would allow them to employ staff, set admission arrangements and own their buildings. More crucially it would distance them from their local authority.
Foundation status had previously only been available to former grant maintained schools.
David Hart, general secretary of the National Association of Headteachers, said: When schools are given the opportunity to go for foundation status, I expect significant numbers to apply."
And among the first to suggest opting out are heads in the partially privatised Hackney, east London, and Rotherham, where three education services are likely to be put out to tender.
Heads in Hackney, where the private firm Nord Anglia has ben working for almost a year, claim there has been no evidence of improvement and that crucial staff have not yet been appointed.
"A lot of heads will consider foundation status," said Angela Murphy, head of Stormont House primary.
Len Wilson, head of Herring-thorpe junior in Rotherham, said: "We need to look at foundation status to see how we can stop being part of this culture of failure."
Some 15 of the 75 councils inspected so far have been judged so weak they need external assistance. Many are in England's most deprived areas.
In Waltham Forest, north-east London, where inspectors found no strategy for education existed, the Government has sent in consultants despite the council employing its own.
Janet Pidgeon, head of Wellington primary, said: "We need to see what happens before we make any decision (about foundation status). Philosophically we want locally-accountable authorities but pragmatically and practically we know they are not working effectively."
Inspection verdicts, 11.