The city council had promised a definitive figure on the cost of the scheme this month, but there will be no public update on the controversial scheme until the end of March as fears rise over the final bill and officials remain in deadlock with the contractors.
The internal mediation between the authority and civil engineering contractors Lagan Construction over the spiralling cost of the Water of Leith Flood Prevention Scheme comes after the bill nearly doubled in a year.
Edinburgh City Council said the setbacks and rising costs were due to bad weather and unforeseen land conditions.
Environment leader Lesley Hinds pledged the scheme would be complete by autumn 2013, but there are concerns it could now run into 2014 as deadlines continue to be missed, and the prospect of further hindrance caused by poor weather looms.
Council officers are challenging the bill, which council papers confirm stands at £21 million including fees for consultants yet to be publicly identified.
It is up from £11.5m originally budgeted, and the project is now more than a year late.
A raft of compensation claims have been lodged with the council by residents living in Stockbridge and Bonnington, who have suffered damage to their property by the massive civil engineering project.
Some who have had damage to their property are on the first floor and have never been troubled by flooding.
The council has been criticised for allowing open-ended contracts after the city's trams project – for which costs rose from £545m to £776m – was halted for months while officials and contractors tussled.
The scheme was initiated after about 500 properties suffered flooding from the Water of Leith in 2000, costing an estimated £25m of damage, but some believe the project on its current scale was not necessary.
One resident said the works, including pile-driving, "sent shockwaves through adjacent flats which literally shook them to their foundations".
Nigel Bagshaw, Green councillor for the area, said: "I am concerned about the time and cost slippage involved, and the lack of up-to-date information that has been made available. The residents along the Water of Leith in Stockbridge and Canonmills have a right to know when the works will be completed and their lives can get back to normal, and the people of Edinburgh more broadly are entitled to know when the dispute is likely to be resolved and what the final cost will be.
"The last thing we want is another tram-like fiasco with work stalled by poorly managed negotiations and increased expense for the Council.
"As I have said before, the city needs to look again carefully at the type of contracts it signs in order to protect itself against any unreasonable claims."
A council spokesman said: "As mediation is still ongoing between the council and the contractor, a report will not come before the committee until March 19 to allow that process to reach completion, although elected members will be getting a briefing on where things are at with the Flood Prevention Scheme in February".
A Lagan Construction spokesman declined to comment.