Police headquarters are on South Burhans Boulevard between West Franklin and West Washington streets.
Jones said Thursday the department needs more room for its crime lab, women's locker room and computers and could use additional meeting and interview rooms.
If the police department were to move into the Baldwin complex, it might be possible to establish a central booking and detention area that would serve city police and the Washington County Sheriff's Department, he said.
The location would be convenient because it would be close to a new District Court building planned for West Antietam Street, he said.
The police department would need about 100 parking spaces for police, employee and visitor parking, Jones said.
Councilman Lewis C. Metzner said the Grand Piano warehouse could be razed for parking and the nearby parking deck could be used. A pedestrian walkway could be built from the deck to the complex, he said.
Fire Chief Gary Hawbaker said fire officials are happy in the Farmers Market building behind the YMCA off Church Street.
The fire department has been there since 1985 and expanded its offices in the late 1980s when the signal department relocated, he said.
The building has room for a ladder truck or engine if necessary, Hawbaker said. During the day, up to eight fire department vehicles are parked at fire headquarters.