The Santa Ana City Council last week directed city staff to explore the pros and cons of such an ordinance, according to the Orange County Register.
One councilwoman wants the pay boost for workers in companies that have at least 300 employees nationwide, with at least 10 workers in each store, the news outlet reports.
The proposed boost in pay could be in effect for about four months.
Meanwhile, officials in Los Angeles County are considering a similar proposal.
The Board of Supervisors is looking into a motion that would require national grocery and drug retailers operating in unincorporated areas of the county to pay frontline workers an additional $5 per hour in "hero pay."
Earlier this month, the board voted 4-0 to request the drafting of the hero pay ordinance, with final approval possible as early as Jan. 26. If approved, the hero pay ordinance would remain in effect for 120 days.