Matthew Smith, 34, a student and founder of Sheffield Libraries SOS, set up the petition on February 1 and it has gathered 95 signatures in support of his campaign to abolish volunteer libraries and library fines so far.
But Chris Brown, 72, Chair of Greenhill Community Library said the idea of handing libraries back to the Council is offensive to the volunteers who have tried so hard to keep them alive.
Mr Smith said: "I don't think volunteer libraries have benefited anyone. You look at the number of people that's using volunteer libraries and they're as
good as shut.
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"The Council view libraries as perfectly acceptable to be run by volunteers. They've shifted the blame and responsibility for running these libraries onto local communities."
Mr Smith argued that Sheffield City Council should follow the Leeds model, which has 33 staffed libraries under Council control. He added: "You're supposed to be opposing this austerity and all you're doing is implementing it. If it's acceptable to run libraries with volunteers why not schools or hospitals?"
Only 12 libraries in Sheffield remain controlled by Sheffield City Council. Sixteen local branch libraries which faced closure in 2014 are now run by volunteers.
But Mr Brown said: "I think it would make things considerably worse.
"We're not sitting here giving palliative care to this library; keeping it comfy while it gradually dies. It's been reborn.
"I'm very protective of the morale of our volunteers, I think this has the potential to damage that morale."
Cllr Mary Lea, the Cabinet Member for Culture, Parks and Leisure, claims Sheffield's current library system is working well.
She said: "The model has proved to be successful.
"It is unlikely that we would return to a situation where all of Sheffield Libraries were brought back within Council control.
"We have been looking into the implications of taking away library fines for the late return of library materials. This is constantly under review and will be looked at again."