Council approved the staff report Monday night. It emphasized the council supports a ban, but said it should be regulated by the federal government.
The report was commissioned after the Vancouver Animal Defense League took the case for a ban to the council in June last year.
League spokesperson Anthony Marr is worried waiting for a federal ban will take too long.
"The scientific community is saying these severely endangered species could be gone by 2017, so there's really no time to delay.
"If we really care for the health of the planet, our children's future, we have to ban right now."
Seven Lower Mainland municipalities have enacted ban bylaws.
Burnaby, along with Vancouver and Richmond, still permit the sale of shark fins.