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 – equivalent to 18 full-time staff.
Coun Dave Allen Derbyshire County Council cabinet member for health and communities, said: “The option to keep two vehicles received the greatest support and many respondents said they’d rather see the frequency of the service reduced than not have one at all.
“We’ve taken these comments on board to develop the second stage of our consultation with a proposal which would make a significant saving while still operating two vehicles on a monthly timetable.
“But I need to stress all options remain open and we’re keen to hear a full range of responses and fresh ideas.”
Questionnaires are available in all county council branch and mobile libraries and GP surgeries or can be completed online at www.derbyshire.gov.uk/mobilelibraries
For more information about The Derbyshire Challenge visit www.derbyshire.gov.uk/challenge