Spokesman Richard Maher said the government has launched a study to determine whether it would be feasible to close the facility at 316 Olive Ave., which was built in 1935.
If the office closed, its delivery staff would be relocated to another post office. P.O. boxes and retail services would also move to a different facility.
If the study shows that the office can be closed, the Postal Service will hold a public hearing.
"No decisions have been made," Maher said. "We're not sure if this would be able to be accomplished."
The post office, a Works Progress Administration project during the Great Depression, opened on Dec. 7, 1935. According to local historian Chris Jepsen, it was designed by Louis A. Simon, who designed the federal courthouse in downtown Los Angeles as well as post offices in Canoga Park and Whittier.
The interior walls feature photos of its construction as well as the program from its dedication ceremony.
Maher said the Postal Service has sold a number of offices nationwide in recent years to cut costs. With a site like the Olive office, he said, the government could insert clauses in the lease mandating that the new owners maintain the historic nature of the building.
Celeste Hamil, a marketing consultant for the Huntington Beach Downtown Business Improvement District, said a closure of the post office would be a loss to the neighborhood. The building is such a local landmark that a few months ago, comedian
"A lot of people come down here and use that post office," she said.
In 2009, the Postal Service put the Olive office on a list of national locations that were slated for possible closure due to lack of funds, but it has remained open since then.