Villagers are being asked if they are prepared to pay an extra fiver a year to keep their local library open.
Burbage library is one of 36 community facilities countywide which could close under planned County Hall cuts.
The county is asking communities to come with up with their own plans to run them themselves with their support from next April.
If no volunteers can be found, they could be shut and replaced by a weekly mobile service.
In response, Burbage Parish Council has launched a consultation on a possible community takeover of the £24,500 a year service in the village, which had 16,300 visitors last year.
Parish council chairman Richard Fleming said: "Our library is a valuable resource and is well used by the residents of the village, particularly by children. It would be a great loss if it were to go.
"We understand that the county council is having to cut £800,000 from its libraries budget – that is why we, as a parish council, are asking people what they would like.
"We do not want to prejudge the outcome and are asking if they would be prepared to pay an additional average contribution of £5 a year or volunteer their time to help run it."
A questionnaire has been published in the village newsletter and the council is hoping to get widespread feedback from the village's 17,000 residents by September 30.
In the past 12 months, Burbage library recorded 16,300 visits involving 17,778 loans. There were also 819 computer user sessions.
Mr Fleming said: "I was pleasantly surprised to see how well used the library was, considering it is only open for 14 hours a week."
Should a local team take over the library, it could expand its opening times and encourage wider use of the building.
At the moment, the library is open on Mondays and Tuesdays from 2pm to 5pm, Thursday 10am to noon and 4pm and 7pm and on Saturday from 10am to 1pm. It is closed on Wednesdays and Fridays.
County council libraries spokesman Richard Blunt said: "We are very keen to hear what people in Burbage – and the rest of the county – think about our proposals.
"I know that people value their libraries and want them to continue, as community hubs. A number of groups are already looking into how they could manage libraries and we are keen to work with them."
He said that the county council was having to save £800,000 per year from its £5.6m libraries budget.
It is proposing to reduce opening hours at the 16 most-used libraries and assist communities to run the remaining 36. The consultation results will be considered by the cabinet in September.
People in Burbage can give their views to the parish council by post to the Millennium Hall, Britannia Road Burbage LE10 2HF or e-mail:
julie@burbage-council.co.uk
Libraries under threatThe 36 community libraries under threat are: Anstey, Barrow, Barwell, Bottesford, Braunstone Town, Burbage, Castle Donington, Countesthorpe, Cosby, Desford, East Goscote, Enderby, Fleckney, Glenhills, Great Glen, Groby, Hathern, Ibstock, Kegworth, Kibworth, Kirby Muxloe, Leicester Forest East, Market Bosworth, Markfield, Measham, Mountsorrel, Narborough, Newbold Verdon, Quorn, Ratby, Rothley, Sapcote, Sileby, South Wigston, Stoney Stanton and Thurmaston.
The council's 16 most-used libraries are at: Ashby, Birstall, Blaby, Broughton Astley, Coalville, Earl Shilton, Glenfield, Hinckley, Loughborough, Lutterworth, Market Harborough, Melton Mowbray, Oadby, Shepshed, Syston, and Wigston Magna.