The council's chief finance officer, Neil Warren, said on Monday that that amount was needed "just to stand still".
It comes as annual council tax bills for local households could be set to rise by a minimum of £40 a year.
The local authority's Budget proposals, which include the rise and will go out to public consultation this week, have outlined a £32m hole in its finances.
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It will likely be covered by a combination of hiked council tax, cutbacks to council services and dipping into reserves.
The Labour-run council's bosses have criticised the government for not "adequately" funding local authorities, despite ministers claiming this year's funding package for councils is the biggest in a decade.
Speaking at an audit committee meeting on Monday, Mr Warren said the council's costs were naturally rising steeply.
He said: "It will cost us something like £15m just to stand still next year.
"By standing still, that recognises the cost of inflation and things like rising energy prices as you would expect.
"We also have to take into account the increase in National Insurance employers' contributions and also the increase in the National Living Wage.
"The increase in the National Living Wage is absolutely a good thing, but unfortunately it doesn't come with funding from the government to be able to match that."
Although the council started last year with reserves technically totalling £175m, the overwhelming majority of it is ringfenced for certain things, or comes from government grants which can only be used after a fixed period of time.
In reality, £15.4m has been set aside in general reserves to be used in emergencies.
Mr Warren said there was a "balance" to be struck, between maintaining a strong amount of savings and investing where necessary.
He said the council eventually wanted to get to a stage where they had a "sustainable budget", which does not have to be propped up by cash from reserves.
He told councillors: "Our reserves are relatively healthy compared to others.
"I'm not saying we've got the most by any means, but I'm comfortable with the levels we've got."
Local Democracy Reporting Service