The board's three-member Rules Committee is scheduled to vote on a proposed ordinance introduced by Supervisor Chris Daly that would make the zoo's primary mission to house and care for both exotic wildlife and domestic animals rescued from inhumane care.
Animal rights groups called for the change earlier this year following December's fatal mauling of a zoo visitor by an escaped tiger and the deaths of zoo elephants in earlier years. They have also claimed animals at the zoo are kept in inhumane, "third-world" conditions.
Zoo officials have repeatedly denied those claims.
The law would allow the zoo to continue breeding programs for certain exotic species such as gorillas, African lions, Sumatran tigers and giraffes.
It would also create a Zoo Animal Welfare Oversight Committee, tasked with holding public meetings on animal welfare at the zoo and advising the Board of Supervisors.
The three-person committee, of which Daly is a member, will consider the ordinance at its meeting at City Hall Thursday at 10 a.m.
If approved, the proposal will go to the full board for consideration.