The Star-Herald reports that part of the jail site is located inside the city limits on property zoned as residential.
Mayor Jimmy Cockroft and building inspector Brent Busbea have proposed rezoning the property to commercial.
County Supervisor Charles Fancher told the board of aldermen this week that the county has needed a new jail for a long time.
"I know that no one wants it in their backyard and I wouldn't either. I, for one, don't want to stand in the way of this jail being built because it is needed. If we don't build one, we are going to have to send our prisoners somewhere else.
"This is our last resort. If we don't do this, we don't have any other place in the city limits to do this," Fancher said. "It's just that plain and simple."
Board of Supervisors Attorney Scott Pickle said an attorney general's opinion says the jail must be built within the city limits of the county seat.