The council will take up the proposed ban at a meeting on Tuesday.
If an outright ban passes, the penalty for violators would be a $500 fine and up to six months in jail.
A second offense would carry a penalty of a minimum of ten days in jail.
The director of public safety would be able to give written exemptions to individual sex offenders.
The second option -- limited to sex offenders whose victims were children -- would involve similar penalties but offer no exemptions.
In April, the Orange County Board of Supervisors voted in favor of an ordinance forbidding registered sex offenders from visiting county parks.
Since then, the cities of Costa Mesa, Huntington Beach and Laguna Beach have all considered enacting bans.
And in May, Westminster made it a misdemeanor for registered sex offenders to visit parks.