Regional chambers want to take full advantage of DTLR draft procedures giving them a bigger role in nominating members to the Committee of the Regions.
But the LGA fears the regions will nominate too many men, too few political parties and neglect small councils. It wants the power to refer regional nominations back if they do not meet political or gender balance criteria.
The dispute is seen an augur of future conflict over how English devolution, should it take off, may disadvantage areas or groups within regions.
Districts and independent councillors might be excluded unless the association had a role in the selection process, he added.
East of England Local Government Conference policy officer Colin Robertshaw said his region was asking for top-up members to be drawn from a pool nominated by the regions.
'I understand colleagues in other regions are attracted by that idea as well,' he said.
A paper for the LGA executive meeting this week said discussions between the association and its regional groupings had not 'helped resolve the problems'.
For example it was clear 'any suggestion that regional places which did not meet criteria of balance might be referred back by the LGA would be badly received'.
Local Government International Bureau director Jeremy Smith said: 'There's a lot of interest in this, a lot of members want to be on the CoR.'
The deadline for submissions on the draft guidance was today (Friday). Whatever the procedure's final shape, nominations will be vetted by ministers.