The General Services Administration has announced it will sell an unimproved 1.4-acre portion of the sprawling Franconia Supply Depot near Springfield Mall in a sealed-bid sale this May.

The parcel, in an industrial enclave, is immediately south of Spring Mall Dodge on Loisdale Road.

It is the second tract of federal property in Northern Virginia to be offered for sale under President Reagan's land-sales initiative, which is designed to raise money to help offset rising federal deficits. The other parcel, sold in January for $33,500, was in Prince William County.

Earl C. Jones, GSA's assistant commissioner for real property, said the sale was a routine disposal of unneeded property.

"Now, I can't talk about how much it is worth, but I hope with the mall and all nearby, that it's worth more than we bought it for," Jones said. It was acquired in 1965 for $112,000.

The remaining 71.2 acres of the Franconia supply complex is undergoing a review to determine if the property is underused and should be sold. B. Michael O'Hara, director of technical services for GSA, said "we are looking to see if there is any more land there that could be disposed of, and our survey will be completed within a week."

GSA land sales officials said they doubted that the facility would be declared underused since another part of the agency, the Federal Supply and Services, opened a new personal property center there this week. That center is designed to expedite the transfer of furnishings between agencies that don't need the items and those that do.

Last year, GSA opened a new furniture refurbishing center at the warehouse complex, as a central clearinghouse for the repair of damaged furniture. The center coordinates repair contracts, including one with prisoners at the Lorton Reformatory. There are about 180 federal employes now working at the Franconia warehouses.

The 1.4-acre parcel was officially declared excess to GSA's needs on Aug. 24, 1982, and after being screened for use by other federal agencies, it was declared surplus to the federal government on Nov. 19.

There are no other parcels of Northern Virginia property that are now likely to go on sale at least until summer, Jones said. There are three other parcels, however, that have been deemed "excess" by the agency controlling them, and given to GSA to screen for other federal agency uses and for public benefit conveyances. The three:

* 107.2 acres at Fort Belvoir that once was under consideration for use as a Virginia state prison site.

* 16.5 acres in Arlington known as Barracks K, adjacent to Arlington National Cemetery. The tract, now a parking lot, has been in GSA's disposal inventory, Jones said, "for years and years. We have no active plans to dispose of it right now because of all the local interest . . . and controversy."

* 11.4 acres, and nine buildings in Fairfax County that used to be part of Nike Battery W-74.