The George P. Hyman Construction Co. of Bethesda stands to lose a $58 million federal construction contract next month if the General Services Administration decides to heed the advice of its New England regional chief and scrap a planned federal office building in Boston.

The Hyman Co. won the contract for the 11-story building in January.

The concrete and steel tribute to House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) became a political football in recent weeks because word that the building was on thin ice leaked to the Boston media. The media promptly turned the fight into a Reagan-administration-vs.-the-local-Democratic-congressman spat.

Meaning the project to be a cornerstone of the North Station Redevelopment Project, Congress ordered GSA to plan construction of the building in 1978, and the agency has spent several million dollars on planning and design work.

But regional administrator Porter D. Leighton wrote to his GSA superiors here last month that the building isn't needed because there aren't enough federal employes located in leased space in the region to fill the 468,914 square feet of office space in the building.

GSA Public Buildings Commissioner Richard O. Haase sent a personal emissary to Boston to survey the space needs and apparently has reached the conclusion that Leighton may need spectacles because there are two dilapidated federal buildings--a Customs building and a VA clinic--that should be evacuated and the people consolidated, perhaps in the new O'Neill Building.

Fouling up the scenario has been a delay by Boston city officials in getting the site of the building available for transfer to GSA. Only recently did the city raze an old hotel on the site, and still must clear the lot. If the property isn't ready by May 6, the deal is off, Haase said. And on May 12, the bid submitted by Hyman must be accepted or it expires.

Meanwhile, Boston Globe reporters have quoted O'Neill as saying he didn't care if the building went up or didn't.

GSA has put up for sale a portion of the John H. Kerr Dam and Reservoir Project in Mecklenburg County, Va., and a portion of the Chesapeake and Delaware Canal in Cecil County, Md.

The reservoir project property covers 39.7 acres of unimproved land in a rural agricultural area. Sealed bids on the property are due with GSA by June 28. The canal property covers 27.8 acres of unimproved rural agricultural land that is suitable for residential development. Sealed bids on that sale are due with GSA by June 29.

The only other federal property in the D.C., Maryland and Virginia region that is now on the auction block is an acre that is part of the Franconia Stores Depot, a GSA warehouse in Springfield. That sale is scheduled for May 25.

So far in the first year of the Reagan administration's federal land sales program, three parcels in Virginia have been sold for a total of $39,123.

There have been no sales in Maryland.

One attempted sale in Washington, the Wilburn Family Housing Annex to Bolling Air Force Base, ended after GSA failed to persuade the high bidder--William N. Cafritz of Bethesda--to increase his bid to the fair market value of the property. Cafritz bid $83,330 for the tract, at Fourth and Trenton Sts. SW. It was the fifth time in the past three years that GSA had tried to sell the Wilburn Annex. In 1981, GSA received a bid of $254,000 for the property, which it also rejected as below market value.

Here's what else is available in May from GSA.

MAY 12: Fifty-three acres of agricultural-residential property and 38 buildings on former Nike Missile Sites No. 5 and No. 6 at Waianae, Hawaii.

MAY 17: A 4.6-acre urban-industrial property with one building at a supply depot in Jeffersonville, Ind.

MAY 18: A seven-story warehouse on a 4.2-acre lot at the Hunters Point Naval Shipyard in San Francisco.

MAY 24: An 11.4-acre residential property on the San Gabriel River in Los Angeles County, Calif., and a 31-acre residential property including 16 buildings on the former U.S. Agriculture Department Date and Citrus Station in Riverside County, Calif.