The administration hopes to select a bidder and get City Council approval by Dec. 5, with work to be completed in 2015.
With the $50 million overhaul of Dilworth Plaza nearing completion in the next year, that means the two great civic spaces at the city's core could be reborn by the time Nutter leaves office in early 2016.
Money from the sale of the garage likely would be plowed into the city's debt, especially the underfunded pension system. For years, Nutter and Council have been talking about selling various assets - such as the Philadelphia Gas Works - to pay down those obligations.
Through his spokeswoman, Council President Darrell L. Clarke said he was "pleased to see the administration moving forward on the sale."
The four-level garage is in dire need of repairs and an aesthetic spruce-up as well as work to make it handicapped-accessible. A 2006 assessment put the cost of the work at about $7.5 million.
Any buyer would be required to make a number of upgrades, including installing an elevator.
Budget Director Rebecca Rhynhart said it was too early to tell how much the city might get for the garage or how many bids would be forthcoming.
Robert A. Zuritsky, president of Parkway, the Philadelphia-based parking and real estate development company, said he hoped to bid.
He said the garage's problems were "repairable" and he didn't think its condition would scare off bidders.
"It's a very, very exciting opportunity," he said. "They're going to get a lot of interest."
From 2010 to 2012, the garage generated about $3.2 million in revenue each fiscal year, according to the city.
LOVE Park, built in 1965, has been showing its age, especially since the Benjamin Franklin Parkway was given a face-lift.
The city would spend most of 2014 midwifing the redesign with public input, Rhynhart said.
"This is a major public space in the center of the city," she said. "That's why we have that year of design work."
Mayor Nutter first discussed a $20 million renovation of LOVE Park last year. The proposal was scaled back in budget discussions with Council, and the 2013 capital budget contained $6 million for the project.
The rest of the money has been budgeted in the Council-approved six-year capital program, and the remaining $10.5 million would be allocated in next year's capital budget, Rhynhart said.
The city would retain control of $2.7 million of the renovation budget for rehabbing the welcome center and untangling the garage utility systems from those of the Municipal Services Building.
Contact Troy Graham at 215-854-2730 or firstname.lastname@example.org, or follow on Twitter @troyjgraham.