"Anything that saves money is important, every dollar is important," said Councilman Tom LaBonge.
City council members want to hear proposals from private companies and nonprofits that could operate the zoo for less.
Salaries, pension costs and health care for city employees have risen, but admission prices have stayed the same to ensure all income levels have access.
Labor groups say they want entrance fees to be affordable, yet they are worried about keeping their jobs.
"We have to really almost kill ourselves to get everything done, to do the things that we feel are important that they cut out, like for example training or enrichment," said zookeeper Amy Rosson. "We really don't have a lot of time for those kind of things with the staff that we have in place now."
The city has already made cuts - 15 percent of the staff was laid off in the last 3 years.
Under the so-called alternative management structure, none of the zoo's 228 full-time workers would be laid off. Employees who do zoo-specific work would keep their current jobs. However, plumbers, carpenters, gardeners and other non-zoo specific employees could be transferred into other city departments.
All new hires at the zoo would work for the new private manager.
Animal advocates are pushing for an option that would keep zoo management in the city's hands. It would give them more power as watchdogs.
Rock musician Slash of Guns 'N Roses, who serves on the zoo board, weighed in on the debate.
"It's been done all around the country, and done really well by some very famous zoos, as far as privatization is concerned, so that's what we are striving to do," he said.
City leaders stress that the zoo will remain the city's property. The aim of a partnership is to keep animals and visitors happy while maintaining financial health.
Without an effective plan, the city's chief administrative officer has already warned the council that there could be more cutbacks, or even closure.
City News Service contributed to this report.