Parker Center, the Los Angeles Police Department's storied headquarters for more than half a century, would be demolished under a plan introduced Tuesday.

The fate of the structure, which is considered worn down and outdated, has been uncertain as the LAPD pursues construction of a new 500,000-square-foot facility across from City Hall.

Councilwoman Jan Perry, who represents much of downtown, introduced a motion calling for the city to study the feasibility of tearing down Parker Center once the new facility opens to make way for new city offices.

Perry said she introduced the plan now because there are numerous developments in the works in the Little Tokyo area surrounding Parker Center.

Named for Chief William Parker, who died in 1966, the structure is only the second headquarters the department has ever inhabited, said Glynn Martin, executive director of the nonprofit Los Angeles Police Historical Society.