A trade union says library staff are "angry and upset" as a council considers transferring the service to a social enterprise.
City of York Council has approved the development of a business plan for what it calls a community benefit society to run the city's 13 libraries.
Unison said it opposed the use of social enterprise schemes in public services and staff were concerned.
The council said staff would be fully involved in the scheme's development.
The Labour-run authority is cutting £250,000 from the library services budget in 2013-14 and said looking at options for sustaining the service in the future was essential.
Fiona Williams, head of City of York Council's library service, said: "In these difficult times we would be remiss if we weren't looking at lots of differing options for how we provide services.
"We've looked at it [community benefit society] and we believe it may offer some advantages."
The council would still fund the service through an annual fixed grant but as a social enterprise with charitable status, it would be able to attract other sources of funding, said the authority.
Andrea Dudding, general convenor for Unison in York, said it was not clear what type of grants the service might be able to access.
"We are opposed to social enterprises in public services in principle.
"Libraries are a statutory service and have to be comprehensive and efficient and outsourcing means the council has no control," she said.
She added: "Staff are very upset and angry and haven't been consulted about it."
The council said it had been talking to staff about the idea of a social enterprise for over a year and more talks would be held as the business plan was developed.