Chief executive Brian Briscoe is anxious to avoid a period of uncertainty after polling day on 6 May, when clear political leadership will be crucial to the LGA's presentation of an effective case in parliament during the passage of the local government Bill.
It seems almost certain Sir Jeremy Beecham will remain as chairman, at least in the short term, as there is no open challenger from within his Labour group and there is little chance of the Liberal Democrats, Conservatives and Independents joining forces to oust him.
But it is possible Sir Jeremy will relinquish leadership of the Labour group, although he is not keen to do so. This would probably result in a contest for the vacancy between Kirklees MBC leader Sir John Harman - seen by many in the group as the natural successor to Sir Jeremy - and Len Duvall, the ambitious leader of Greenwich LBC who fronted the LGA's reorganisation of the Local Government Management Board.
The smaller groups want to use Labour's expected loss of dominance to press for a greater degree of cross-party working in the LGA. Options being discussed include having the leader of the second largest party - presumably the Conservatives - as vice-chair.
The degree of power-sharing on the committees will depend on the relative strengths of the parties. If they are fairly evenly balanced, a radical option being floated is to divide up committee chairs according to party strength.
An alternative would be to have vice-chairs of committees being drawn from the three opposition groups. Any decisions along these lines would entail the party groups exercising a lot more central control over the allocation of posts on committees. At present, each committee is left to elect its own officers.