The association, which represents the heavily Labour-dominated metropolitan councils, wants Labour to keep the controversial Office for Standards in Education together with the inspection teams set up under its wing.
But the association is proposing that schools and local education authorities should be given a bigger role in checking their own standards, with OFSTED responsible for supervising procedures and rubber-stamping local schemes.
The plan comes as OFSTED carries out its own review after falling behind with plans for inspecting all schools every four years. Primary school heads have been co-opted to join HMIs in an attempt to bring the programme up to date, and in a consultation exercise now taking place, OFSTED suggests allowing schools deemed to be satisfactory to be inspected every six years instead of four.
The AMA says its proposals, far from heralding a more relaxed attitude towards schools, are aimed at ironing out uneven standards in the current system which depends on OFSTED-registered team leaders tendering for school inspections on the open market.
The proposed measures would also cut bureaucracy and are aimed at maintaining the current four-year cycle, the AMA says.
The association's report was welcomed this week by Labour education spokesman David Blunkett as a "useful contribution" to the debate over school inspections.
It coincides with further controversy surrounding the chief inspector, Chris Woodhead. Speaking to MPs at the Commons select committee on education, he accused headteachers and governors of lacking the will to dismiss 15,000 allegedly incompetent teachers.
In its report the AMA says primary responsibility for standards rests with the staff, headteacher and governors working in partnership with parents.
Schools should regularly review the quality of education they deliver and produce an annual "self-assessment report" and action plan to bring about improvements.
Local education authorities would have to produce plans to inspect all their schools once every four years. At least half the inspections of secondary schools and 25 per cent of primaries would be carried out by teams external to the authority.
All teams would have to be accredited by the national inspection service to make sure their members are experienced and properly qualified and trained. But the current tendering process, in which teams of inspectors from the pubic and private sector compete for contracts, would be abolished and payment would be according to a nationally-set scale of fees.
Schools with serious weaknesses would be given a one-year probationary period to improve before being labelled "failing".
John Merry, chairman of the AMA working group on school inspection which produced the report, said: "The overall aim is to preserve the four-year inspection cycle which is in danger of collapse."