Council chief Ian Floyd says the organisation has an £8 million funding gap.
He said the council is consulting with trade unions and staff affected by plans to cut jobs, which could lead to "20 or more redundancies over a 90 day period".
The Press asked what departments could be affected by the redundancies and if frontline workers' jobs are at risk, but the council did not say.
Ian Floyd, chief operating officer at City of York Council, said: "We are currently collectively consulting with our trade union colleagues and those staff affected on a number of proposals and as such have made the appropriate notifications as these proposals could result in 20 or more redundancies over a 90 day period.