A consultation paper written by Mr Briscoe proposes that these top-ranking directors would form the new association's board of management.
Apart from the Welsh Local Government Association secretary's post, which has been filled, they would include:
-- A deputy chief executive
-- A director of management and membership services
-- A director of local government finance.
The office of the chief executive would also answer directly to Mr Briscoe but would be headed by an assistant chief executive.
The director of communications will be chosen at the end of this month from a shortlist of three: Carol Grant, a freelance housing consultant; Peter Kendle, who has worked for Eurostar; and Nick Gammage, a Department of Health press officer. The post was advertised at £70,000 a year on a short-term contract.
The only other appointment so far made to the new association is Steve Bullock as policy officer to the LGA's majority Labour group.
The deputy chief executive would head the LGA's policy and research efforts, including the co-ordination of temporary policy task forces.
This officer would also direct five professional advisers - on topics such as education and social services - who might be recruited on secondment from councils.
It is not yet clear how many senior posts there will be in the new structure to support the five main directors.
Mr Briscoe suggests he retain responsibility for lobbying with Parliament, Europe and other countries and guidance to the Local Government Management Board on pay negotiations.
Mr Briscoe said existing association staff would be able to comment on the paper this month before either he or LGA members made any decisions on the association's structure in September.