MONK Bretton library is set to close.
The crumbling building - which requires extensive, expensive repairs - has seen the number of visitors plummet over the last year.
A four-week consultation process has started, asking its users how they would be affected if the library closed.
Coun Jenny Platts, cabinet spokeswoman, said: "We want to continue to provide a library service for the people who live in Monk Bretton.
"Unfortunately, the current library building is no longer fit for purpose. At this time when the council is facing significant cuts, we simply do not have the funds available."
People can take part in the consultation, which ends on August 9, by picking up a copy from the library.