At a meeting of its full council on Thursday next week, North Lanarkshire Council's membership of the Convention of Scottish Local Authorities (Cosla) will be debated.
If a majority of councillors signal they wish to leave the organisation, North Lanarkshire would be likely to become the eighth Labour-led council to decide it wants to formally withdraw.
Glasgow, Aberdeen, South Lanarkshire and Renfrewshire are among the authorities that have already indicated they want to leave Cosla, plunging the organisation into crisis.
The row centres on issues of where the power lies within the organisation, how funding to local authorities is distributed and the overall effectiveness of the body.
A Cosla spokesman said last night: "North Lanarkshire Council is and remains a member of Cosla.
"Hopefully they will make the same decision next week as Moray did yesterday to stay in."