Councillor Ian Brookfield said the authority is in a “slightly better” position than in previous years, but warned cuts would still have to be made.
It comes as the city’s budget deficit stands at £3.9m for 2020-2021, with bosses considering a range of options to bring the figure down.
Councillor Brookfield said the current strategy could change in the "coming weeks and months" if an election was called – with the authority's books continuing to be monitored.
He said: "There's no crippling cuts this year, but there are cuts remaining – it's slightly better than previous years, but it won't make up for years of savage cuts.
"We would much rather have had years of not having to make cuts."
It comes as the council looks to tackle a deficit of £20m by 2023-2024.
Council tax will likely be raised by 1.99 per cent, or £36 for an average property in band D, in 2020-2021 as part of the cost-cutting plan.
It could increase further, however, with consultations taking place by the Government to increase the social care precept by two per cent.
One-off funds totalling £1m will be released from the Job Evaluation fund – with £500,000 from the Equal Pay Provision money pot.
Government grants for adult social care, education and skills, and to tackle rough sleeping will be used as part of the plans.
Cuts worth £220m have been made since 2010-2011 in the city, a report to the council's cabinet said.
It added: "The extent of the financial challenge over the medium term continues to represent the most significant challenge that the council has ever faced, with reducing resources, growing demand for services and significant cost pressures."
A formal budget consultation will take place between October 21 and December 31, with the public's views sought.