The consultations, which will affect areas like Clowne, Creswell and Whitwell, is the second stage of a consultation to help the authority deal with budget cuts.
The council has to cut £157 million over the next five years and its mobile fleet currently consists of two large maximum capacity vehicles (MCVs) and eight smaller standard mobile libraries.
It costs the authority £720,000 a year to run the service which currently employs 26 people.
Thousands of residents took part in the first stage of the consultation earlier this year and gave their feedback on a range of options, including to stop the service completely, withdraw some mobile vehicles or to encourage community groups to provide the service.
Their comments have now been used to develop a more detailed second stage of consultation outlining a proposal to maintain two standard mobile libraries working to a monthly timetable.
Further comments on the full range of options and alternative suggestions continue to be welcomed until 9th August.