Owners of many tobacco and e-cigarette shops in Lexington said they let people smoke these devices inside their shops. If the ordinance passes, this would not be legal.
Residents also would not be allowed to use e-cigarettes at restaurants, bars or other public establishments.
This is the second reading of the ordinance. The first reading passed without opposition.
The council meeting is scheduled for 6 p.m.
Governor Steve Beshear has already added e-cigarettes to a ban on smoking on state property. Other cities have similar bans.
If the measure passes, Lexington would be the largest city in the state to ban e-cigarettes.