Blundellsands and Victoria ward Labour Councillors have pledged their support to the new Friends of Carnegie Library.
They are proposing the Area Committee gives £1,000 to the Friends of Carnegie Library to cover essential costs as the Friends put together a business plan to keep the Library open.
Blundellsands Labour Councillor Veronica Bennett said: "The government has forced the council to scale down and withdraw services right across the board. I'm really pleased, though, that the Labour Group has tried to keep open as many services as possible. That includes £1m put aside to support residents and community groups to take over services due for closure under the government's cuts.
"One-thousands pounds from our ward funds will help the Friends of Carnegie Library to put together a robust business plan to access this pot of money."
Victoria Ward Labour Councillors Les Byrom and Mick Roche said they wanted to support the Friends of Carnegie Library to find a way of countering the damaging effects of the Tory-Lib Dem cuts.
Cllrs Byrom and Roche said: "In the face of unprecedented government cuts, changes have to be made. We support community action where it is practical and realistic. We want to show our support for sensible ways of helping local people to formulate possible ways forward."
Local activist Jan Grace, who lives in Crosby, said: "Sefton Council had to cut library funding after the Tory-Lib Dem Government hit the council with cuts for a third year. This year the government took £21.7m from the council's budget and George Osborne has just announced even deeper cuts to our local services.
"I'm delighted the local Labour councillors are supporting direct community action to keep services going. This money will help to build a business plan that could keep Carnegie Library open. I worked closely with Labour councillors in Crosby and Blundellsands to get this proposal for £1,000."