Executive member at Lincolnshire County Council Nick Worth has revealed 18 of 32 under threat libraries have received interest from local communities.
The authority has proposed controversial plans to close 32 of 47 libraries and cut 170 jobs across the county.
It is to save £2 million from the council's budget.
But councillor Worth, executive member for libraries, says he is "staggered" at the positive response he has received from local communities.
Speaking to BBC Radio Lincolnshire this morning, cllr Worth said: "It is not about closing libraries. We want communities to come forward and run them if they can.
"Eighteen of the libraries have had interest and I am staggered by that response.
"What I would say is if people expect their libraries to close then that is most likely what will happen."