Chief executive Oonagh Aitken was expected to give an update of the review which recommended asking Glasgow
City Council, Falkirk Council and Clackmannanshire Council to rejoin the organisation.
Glasgow City Council leader Charlie Gordon (Lab) said he has no intention of rejoining. He is seeking legal advice on issues where COSLA is perceived to be shutting out the renegade councils, such as on joint negotiating bodies.
Falkirk Council and Clackmannanshire Council have said they have no plans to rejoin the organisation, but are more receptive to the idea than their Glasgow counterparts.
Clackmannanshire leader Keith Brown (SNP) said: 'We are in correspondence with COSLA and it is trying to set up a meeting.'
James Shott (Lab), of Falkirk Council, said: 'We have not been officially told anything by COSLA's administration, although there are talks going on behind the scenes.'
Leaders from the three councils have been invited to the meeting, although they no longer pay affiliation fees.
Ms Aitken has invited them to a presentation on the review of chief executives' salaries and they are entitled to stay for the remainder of the meeting, although all three are expected to decline the offer.
The review suggests a cut in the number of elected representatives, and staff are being offered redundancy packages.
The organisation is expected to continue to ask for a minimum affiliation fee while the remainder will be determined on the basis of population. This partly led to Glasgow City Council withdrawing it's£300,000 yearly subscription.