The Society of Education Officers and the Association of Chief Education Officers wants thriving councils to benefit from a "light touch" regime similar to that offered to successful schools.
They are discussing the proposal with the Government and the Office for Standards in Education and hope the new regime could be launched for the second round of counci inspections.
All authorities will have been inspected for the first time by next summer. A date has yet to be set for the second round to start.
However, Graham Lane, education chair of the Local Government Association, representing councillors in all 150 authorities, opposes the move. He said: "I don't agree with 'light touch' as a concept. Schools and local authorities can change quite dramatically in the four to five years there might be between inspections."