Community representatives in Broomhill are to continue to explore ways of keeping open a library in the suburb, despite a bleak outlook.
One idea to be examined is a partnership with the library at the University of Sheffield.
Howard Fry, secretary of Broomhill Forum, said: “We are not giving up, but we are not full of optimism.”
He was speaking after a community meeting at Broomhill Methodist Church drew an audience of about 100.
The feeling was one of “frustration, annoyance and even anger” at the suggestion that the second busiest community library in Sheffield could be closed, leaving only one, at Ecclesall, for the south west of the city.
Broomhill is one of 16 libraries threatened with closure unless community groups or other organisations take them over as the council looks to cut £1.6m from the budget by 2019.
The Taptonville Road library has been earmarked for closure for years because of its poor condition, but community representatives have always believed the council would help find a replacement.
Mr Fry said members of Broomhill Forum had neither the skills nor the time to run a library, and he questioned how community libraries could survive without central support in terms of new books and computers.
A protest, including pupils from Lydgate Junior, is being held at Broomhill library on Monday from 1.30pm to 3pm.
The council continues to consult over its proposed closure programme. The strategy is to retain 12 key libraries, with a further five becoming community-led libraries, with guaranteed council funding for two years, and 11 becoming independent facilities
The authority is now examining ways of giving some financial help to groups interested in running the independent libraries.
Council cabinet member Mazher Iqbal told the Broomhill meeting: “We will look at how we can provide funding for the 11 independent libraries for 12 months.”
He added: “I don’t wake up in the morning wanting to close libraries. I have been out to areas across the city to explain our proposals and I am listening to what people have to say. Groups are asking us to provide running costs.”