Private talks are under way to reach an agreement that brings Clackmannanshire, Falkirk and Glasgow City Councils back into the organisation.
Scottish National Party shadow local government minister Tricia Marwick is to meet newly elected convention president Pat
Watters (Lab) next week to discuss the
Clackmannanshire leader Keith Brown is planning to meet the convention's acting chief executive Albert Tait to discuss the future direction of the organisation and local government in Scotland.
In his inaugural speech, Mr Watters said: 'The 32 councils in Scotland working together are a powerful force. We need COSLA to get back to full membership and full strength as soon as possible.'
Mr Watters promised to redress the balance between local government and the Scottish Executive, a major factor in decisions to quit the organisation.
He said: 'We have to take the lead in shaping the future of local government instead of it being centrally directed. How this can be achieved needs to be investigated as a matter of urgency.
'The opportunity presenting itself is to bring COSLA back to being an inclusive organisation representative of the whole of local government.'
Referring to recent reports that the Scottish Executive is planning a major reorganisation of Scottish local government, Mr Watters said: 'If the Scottish Executive is intent on drawing lines on maps, we cannot stop it.'
Mr Watters is expected to have more success bringing Glasgow City Council back into the organisation as he is from neighbouring South Lanarkshire Council.
An SNP spokesman said: 'We will be discussing the direction of the convention and this could have an impact on whether SNP-controlled councils are part of the organisation.'