But before it can do so, the authority must win a High Court case over its ownership with the original owner's descendants.
The Bridport Area Development Trust was set up two months ago by the Bridport Local Area Partnership with an aim of buying back buildings for community use. The institute is one of its targets.
The trust's interim chairman Tim Crabtree said: "It is a wonderful old building and it is felt something could be done to save it for the community. The challenge is finding a use for it, while creating a sufficient revenue from it, and getting funds together for the refurbishment.
"We also have to wait for the outcome of the court case. If the council wins, it does have a small sum of money for a feasibility study for finding a use for it."
Prof Andrew Rutherford, an independent bookseller in Bridport, said the council told him five years ago that the building needed £1M to fix it.
He said: "They said there has been real deterioration inside. It looks fine on the outside but it could be a different story on the inside."
In 2002, the council spent £40,000 on emergency repairs, such as sealing a leaking roof and securing an upper floor against collapse. The building, which dates back to 1835, was put on English Heritage's Buildings At Risk Register.
It became the Literary and Scientific Institute in 1854-55 and in 1871 was given to the town by Bridport landowner Howard Warburton-Elphinstone, with a stipulation it be used for moral or intellectual purposes.
The potential successors to the Elphinstone estate launched an ownership challenge after the library stopped using the building in 1997.
Town council clerk Bob Gillis said: "The county council has indicated that the building would be surplus to its requirements and that it would welcome interest from other agencies with proposals for the building. It has said that it would want first of all to see a viable business plan for the use of the building."