Talks were held in Downing Street on Monday in a bid to find a solution that may keep a public library open in Market Deeping.
South Holland and The Deepings MP John Hayes and county council executive member for libraries Coun Nick Worth were joined by councillors from The Deepings and members of the Save Deepings Library campaign.
Details of the talks have not been made public, but hopes are high that a rescue plan can be put in place.
Mr Hayes said: “We hope to find a solution that works for all parties and gives the library a viable future.”
Deepings library campaigner Phil Dilks, a Labour county and district councillor, said: “We had a positive meeting and we are looking at the possibilities for a good outcome.
“Obviously I am still determined to save the library and, with goodwill on all sides, there could be a way forward.”
Market Deeping library is one of 30 that the county council planned to hand over to volunteers.