Southwark Council says that it hasn't ruled out repairing the existing swing bridge across the entrance to St Saviour's Dock rather than replacing it with a new structure.
The mechanism which allows the bridge to swing open for river vessels is no long working, so boats are unable to enter or leave the dock.
However, this week's cabinet meeting heard assurances that retention of the existing award-winning structure had not been ruled out.
"We are ensuring that the money is there within the fund, so that if we do have to replace the bridge lock, stock and barrel, we will do that," said Cllr Ian Wingfield, cabinet member for environment and public realm.
"There are still ongoing discussions in relation to repairing the existing bridge rather than implementing a new bridge altogether."
Cllr Fiona Colley, cabinet member for resources, added that while replacing the bridge "may well be the way forward" the matter was not yet settled.
After the cabinet meeting Cllr Wingfield tweeted that the council is obliged to repair or replace the bridge under the terms of the original funding agreement with the former London Docklands Development Corporation.