Internal polling found a quarter of Labour’s supporters in Scotland have switched their allegiances to the Tories since 2015, as the constitution continues to dominate voters’ priorities north of the border.
That could mean Labour losing power at several town halls across its former heartlands, including Glasgow.
Party insiders told The Herald that resources could be focused elsewhere when the election campaign begins in April.
Labour fought hard to retain control of Glasgow City Council in 2011 at a time when many predicted it would fall to the SNP.
But the leaked report suggests many in the party are now pinning their hopes of retaining power on other councils, where coalition deals could potentially be struck with other pro-Union parties such as the Conservatives and Lib Dems.
North and South Lanarkshire councils are both viewed as offering potential life-lines to retaining power.
Labour currently controls - or is lead coalition partner - 16 of Scotland’s 32 local authorities.
Labour MSPs were brifed on the report at Holyrood shortly before their Christmas part on December 21.