Everett Gillison, deputy mayor for public safety and Mayor Nutter's chief of staff, had the project near the top of his wish list as early as 2008.
The national economic collapse that soon followed put the move on hold, but Nutter again raised the possibility in his 2012 budget address.
Gillison last week called the project "long overdue."
"I think this is the biggest investment that has been made in public safety in my years," he said. "It was one of the things I really wanted to make sure we could accomplish."
The new headquarters would allow police to vacate the aging and cramped administration building at Eighth and Race Streets - the legendary "roundhouse."
Although the building is beloved in some architectural circles for its quirky, Brutalist style, the Police Department outgrew its home decades ago.
Pending design work, the plan to move the headquarters west also calls for moving the city morgue - officially, the Medical Examiner's Office - and some Health Department offices to the Provident Mutual building as well.
Then the city would be able to close and sell three buildings, two of them in Center City - the roundhouse, the health offices at Broad and Lombard Streets, and the morgue's building in West Philadelphia.
It would be the latest in a succession of moves across the city's map by major institutions: The Provident Mutual building is part of a 15-acre campus that already includes the city's juvenile detention center - which was moved to five acres there to make room on the Benjamin Franklin Parkway for the Barnes Foundation's arrival from suburban Lower Merion.
Bringing police headquarters and other city agencies to the Provident Mutual building would also infuse thousands of people, working round the clock, into a growing section of West Philadelphia.
Blackwell, who represents the area, called the project "an exciting opportunity," but said the surrounding neighborhoods would have to have input on the development and share in the prosperity.
"Where will they eat? Where will they park?. . . . They may not have worked all that out," she said. "Communities want to know all that."
One thing that's already known: the location's access to public transportation. Police headquarters would be steps away from SEPTA's Frankford El stop at 46th and Market.
Gillison said the plans call for taking the limestone-and-steel building down to its columns and using 3-D imagining to design the interior, down to the fine details, such as electrical runs.
He said he hopes the reconstruction of the building, which dates to the 1920s, can win an emblem of 21st-century thinking: LEED (Leadership in Energy and Environmental Design) certification from the U.S. Green Building Council.
"Great old buildings don't have to be destroyed to have a great adaptive reuse," Gillison said.
Assuming Council approves the two funding bills and a third to transfer ownership of the building back to the city this spring, the project would take an additional two to three years to complete, probably after Nutter leaves office in early 2016.
"I likely won't be around, at least in an official capacity, to cut the ribbon," Gillison said. "Hopefully I'll get an invitation."