Oakland would be the first city in California to enact such a rule.
The goal is to give people with criminal convictions equal access to housing.
Supporters say it's a game-changer, because an estimated 73% of people living in Oakland's vast archipelago of homeless camps have previously been incarcerated.
John Jones III, with the Fair Chance Housing Campaign, called the ordinance "a valuable and immediate solution to the housing crisis."
One mom, identifying herself as Sherry, said her son was forced to couch surf and sleep in his car or on benches because his record prevented him from getting his own apartment.
Some landlords have said they're concerned the rule would give them less control over selecting renters. The California Apartment Association calls the ban the "most extreme housing ordinance in the state." It does not plan, however, to challenge the ordinance in court.
The measure will not only help prevent homelessness among the previously incarcerated, it'll also reduce recidivism by giving people a reason to stay out of jail, said Councilwoman Nikki Fortunato Bas.
"Before getting education , getting a job, getting other opportunities, you need to have a roof over your head to come back to your family, your community, and to put your life back together," she explained.
The ordinance would cover both public and private rental housing, with some exceptions such as federally-funded Section Eight housing, single family homes and homes where the owner is living.
A final Council vote is set for February 4.