The association is keen to debate the framework for the implementation of new freedoms, incentives and rewards for councils, and is to criticise the government's plans to give them earned autonomy.
The system is used in the health sector and involves three-star trusts having access to a list of 10 freedoms and flexibilities.
A briefing paper to be discussed with Mr Byers says: 'The LGA would strongly oppose the simplistic application of this model to local government.'
Earned autonomy ignores the individual political mandate and needs of councils, according to the association.
A spokeswoman for the DTLR said: 'The central/local partnership meeting included discussions about the white paper.
'It was agreed officials from across government should continue to discuss these issues with the LGA.'
The LGA is to demand greater freedoms for all councils which it calls a 'significant bedrock' of deregulation. This includes greater borrowing and trading powers and a reduction in the number of specific grants.
The association suggests the possible introduction of light-touch inspection, an end to ring-fencing, and no direction from the Department for Education & Skills for a smaller number of councils.
Local government minister Nick Raynsford has said high-performing councils should have more spending freedoms and a lighter-touch inspection regime, but only 'where councils have shown their ability to deliver top-quality services and lead their communities'.