CITY council leader Steve Brady says agreement over plans to change terms and conditions of staff at the authority could save up to 400 jobs.
Talks between unions officials and senior council managers over the proposals started before Christmas.
Under the plans, the council would save about £7m a year by slashing overtime and reducing mileage rates.
The authority is facing a £13m cut in Government funding for the coming year.
At a full council meeting, Councillor Brady said striking a deal over terms and conditions would be crucial to easing the impact of the funding cut.
"We are looking to save about 350 to 400 jobs if the new terms and conditions can be agreed," he said.
"Because of what is happening to our funding, I hope our staff will see the sense in remaining in work with changed conditions rather than losing their jobs."
Among the proposals is a reduction in the current 65p mileage rate for staff – 20p higher than rate recommended by HM Revenues and Customs.
Cllr Brady admitted the rate was one of the highest at any council in the country.
"How can we have people driving around on a mileage rate which is even higher than the one which the unions offer to their own employees?"
He said the scale of the cuts facing the council made a nonsense of claims by communities secretary Eric Pickles that his funding settlement for local councils was a fair one.
"We are looking to make sure we have got a local authority that can still function properly and can still do the job of looking after the city.
"However, we have seen a 33 per cent reduction in funding since we came to power.
"Over the next year, there will have to be significant changes in the council structure and we will continue work towards that goal."
He also predicted looming welfare reforms due to be introduced from April would create widespread hardship for low-income households.
Nearly 25,000 households will start paying council tax for the first time while about 5,000 people will see a reduction in allowance payments because they have spare bedrooms under changes to the housing benefit regime.
Cllr Brady said: "I think people are just waking up to what is coming in April and the misery it is going to cause.
"We have not got smaller houses for people to downsize into and where will they get this money from, God only knows."
Opposition Lib Dem leader Councillor Abi Bell accused the ruling Labour group of dragging its heels over publishing details of its budget proposals for the coming year.
She said there was a suspicion it was a delaying tactic.
