Bosses at Kirklees Council hope if enough people come forward it will be able to save them from the axe while reducing costs at a time when it is grappling with cuts in Government funding.
Libraries in Denby Dale, Golcar, Honley, Lepton, Kirkheaton, Shepley and Slaithwaite will be affected.
If the plan goes ahead the libraries will be run by volunteers with support from a nearby council-staffed library.
Coun Shabir Pandor, the council’s joint cabinet member for resources, said: “We want to get people involved in running their libraries and providing what their communities want.
“However, to gauge interest in this project we need everyone to get involved in the consultation and community engagement events. We need to hear what they want out of the service, and how they think it should be run, and how they can help do this.
“Communities will get a real say in what happens in their area. Already a number of community groups have expressed an interest in becoming involved and I am very encouraged by their enthusiasm.”
Local people are to be invited to take a full part in the consultation and the service offered at each of the libraries will be tailored to meet community needs using the results of this.
As a minimum, the community-run libraries would offer self-service books and other media loans, public access computers for accessing the internet, word processing and library-based events. Book reservation and inquiries would be provided through a free phone access to the nearby council-staffed library and information centre.
People who want to get involved should contact their local ward councillors in the first instance.