The Plain Dealer reports the measure was proposed after city audits showed some firefighters lived outside Ohio for months at a time because of overly flexible rules on shift trades. It wouldn't require current employees to move from their homes.
Mayor Frank Jackson has supported the local legislation and said it could help make sure that workers who respond to emergencies are close by.
Part of the measure is similar to a Cincinnati law that was struck down by an appellate court last year. Cleveland administrators say they think the measure would stand up if challenged in court.