Mr Flanagan challenged Mr Gordon for the leadership over what he sees as his dictatorial style.
A spokesman for Mr Gordon said the leader would expect support from an overwhelming majority of the Labour group.
Mr Gordon is furious at suggestions the challenge from Mr Flanagan could be the start of a political war following the publication of a 'manifesto' in which he pledges to negotiate the council's re-entry to the Convention of Scottish Local Authorities.
He said: 'The GHA option sends shivers down my spine. It is too dependent on the whim of large banking institutions and the so-called business plan is unsustainable.'
Around a third of the 74 Labour members are reputedly concerned at the plan to transfer over 80,000 homes.
Mr Flanagan cites violent protests in the wake of the council's decision to close the 100-year-old Govanhill swimming pool (LGC, 6 April) as evidence of policy failure.
The recent murder of a refugee on the Sighthill estate, and resulting criticism of the council's treatment of asylum seekers, has damaged its reputation.
The leadership cannot be challenged until next year's Labour group annual meeting. Mr Gordon has led for two years.