Unison's Scottish convener Mike Kirby said the union will launch a counter campaign when the council begins its tenant consultation on the transfer.
The union says there are a number of issues which remain unresolved, including failure to set up local housing organisations with tenants.
Mr Kirby said: 'Despite being overdue by several months, this document appears not to answer key questions about investment, organisation and running Glasgow's housing service.'
A spokesman for leader Charlie Gordon (Lab) said: 'It is no secret we have, as yet, been unable to complete evaluation of the plan. We will be getting an assessment of the merits of the business plan.' (LGC, 3 August).