The running of Dawley Library is set to be taken on by Great Dawley Town Council. Details of an agreement with officials at Telford & Wrekin Council are being finalised.
The borough council has also made an offer to Newport Town Council that would see the town's library preserved.
It comes after it emerged earlier this week that a deal was on the verge of being struck between Hadley & Leegomery Parish Council and Hadley Learning Community to save Hadley Library.
Telford & Wrekin Council intends to stop running six libraries in the borough as part of a cost-cutting drive to save £30 million over two years.
Councillor Lee Carter, the council's cabinet member for finance and service delivery, said: "While this is not yet finalised, I would like to congratulate Great Dawley Town Council on their positive approach to working in partnership with us to protect services.
"Following on the back of similar excellent news from Hadley, this really does demonstrate a fantastic response from our community at what is a very testing time.
"We are continuing discussions with parish and town councils in other parts of the borough in the next couple of weeks to see what else is possible."
Under the terms of the proposal in Newport, the town council would contribute towards running the library and First Point information services. In return Telford & Wrekin Council would offer a community support officer and an environmental team responsible for duties such as litter.
At a town council meeting last night members agreed to work with the borough council to find a solution. They welcomed the proposals put forward by Councillor Shaun Davies of Telford & Wrekin Council and agreed to vote on the issue next month.