They claim education could be grouped together with housing and social services under a new "personal services" category without its own officer support team.
Brian Briscoe, chief executive of the Local Government Association, is consulting on the officer structure of the organisation, which is to replace the associations of county councils, metropolitan authorities and district councils.
He intends to establish a senior advisory team in key areas such as education and social services.
Mr Briscoe argues in a letter to the three associations that the posts "should provide opportunities for interchange with senior local authority staff and possibly other organisations as well".
The senior advisory team would be supported by teams of policy officers who would be organised on a cross-functional basis, such as looking after education, housing and social services.
The Council for Local Education Authorities last week unanimously demanded that education staffing at the LGA should reflect "more adequately" the size and importance of the service. Councillors said the LGA should have an officer team devoted to supporting the work of its education committee with comparable resources to the AMA and ACC. They argued that education represented more than 40 per cent of local government spending and raised some of the most pressing political issues affecting local government.
Saxon Spence, ACC chair of education, said: "We are going into a new century, with new confidence and new responsibilities. We need to make sure that the new association supports, develops and makes education a service that we can be proud of."