Jim Ouk Song's "Press Express Copy Center" will open within the month in the Vanguard Building at 1925 L St. NW -- hardly an unusual occurrence in a city that has scores of businesses opening storefronts.

But in this case, the block of 945 square feet of space happens to be controlled by the federal government, not the private sector.

The building, leased by the management company of Greenhoot Inc. to the General Services Administration, is primarily used as federal office space by the Labor Department and the Advisory Commission on Intergovernmental Relations. It was fully occupied until budget cuts by the Reagan administration forced the agencies to shrink.

Because Greenhoot is unwilling to reclaim the space and GSA hasn't been able to find another federal agency that needed it, GSA's local utilization branch got it as space that could be "outleased." In April, Jin Ouk Song signed a $34,492.50-a-year lease.

The Copy Center is an example of a blossoming program at GSA that was put together last year to find tenants for vacant space that is at least temporarily not needed by the federal government.

"The goal is to reduce vacant space and to make some money," said George Gross, GSA's national outleasing director. "It is part of this agency's efforts to better manage federal property."

The ever-accumulating blocks of vacant space have been piling up not only because the government's civilian agencies, for the most part, are shrinking, but also because new space-saving efforts designed to shoe-horn each employe into 135 square feet of space, on average, are beginning to be put in place. Having a slimmer, trimmer federal bureaucracy may not mean it will work better, but GSA officials say they are trying to make it cost less and earn more.

"In no way are we trying to be in competition with the private sector," explained Dale J. Bruce, GSA's director of information. "But we are trying to take space that would remain vacant otherwise and turn it into an income producer. That's simply smart management."

Since last October, when Gross' office began keeping outleasing statistics, GSA has snared about $1 million a year in increased revenue business, part of it coming from the 40 new leases and the rest from increased rental charges.

But the totals are far short of the eventual goal. In April 1982, GSA Public Buildings Commissioner Richard O. Haase projected that the program eventually will rent to private business 5.8 million square feet of office space, 6.3 million square feet of storage space, and 1.3 million square feet of special-purpose space.

Through March 31, a total of 994,770 square feet of office, storage and special-use space was outleased -- about 300,000 square feet more than last October. The bulk of it -- 760,704 square feet -- is government-owned storage space, but the tally does includes 118,165 square feet of government-owned office space and 34,607 square feet of commercially leased office space that GSA is subleasing.

"We're running into a market that is as soft for us as it is for everybody else out there," admits Jack Burrows, a regional marketing specialist for GSA. "But we're plugging away."

Still, Burrows proudly notes that although the program is young, the outleasing "take" in Washington -- now $1.16 million a year -- is higher than any other region. Over the past year, Burrows and four co-workers say they have earned the government $687,000 more per year in annual rentals in the outleasing program than was previously collected.

"We stack up pretty well, but we're not being smug about it," Burrows said. "We'll be happy when we reduce the government's rental obligation . . . reduce what we're paying for something that we're not able to use."

As the government's size declines, GSA says it is making a herculean effort to shuffle bodies about to fill government-owned space and relinquish leased space. This back-filling procedure is often dependent, GSA officials say, on finding the right size office group to fit into a vacant space.

"It's extremely important that federal agencies realize that we're moving them in the interest of federal taxpayers and that these moves are carefully studied to determine if they're cost-effective," Bruce said.