The move to build a new prison in Washington appears to be gathering steam, as federal and D.C. officials have begun a preliminary search for a suitable site amid indications that funds for final site selection and design of the facility could be forthcoming as soon as this fall.

Sen. Arlen Specter (R-Pa.) said this week that federal funds may be added to the D.C. government's fiscal 1986 budget, which takes effect Oct. 1, to pay for site selection and design of the proposed new prison, intended to alleviate overcrowding at the Lorton Reformatory and D.C. Jail.

Federal and D.C. officials already have begun looking at sites for the proposed federally financed prison, with special attention being given to seven acres of surplus federal property in the Congress Heights area of Southeast Washington.

The site -- a triangular tract east of Fourth Street SE between Mississippi and Trenton avenues -- is located south of St. Elizabeths Hospital, across the I-295 freeway from Bolling Air Force Base.

City Council member Wilhelmina J. Rolark (D-Ward 8), who heads the Judiciary Committee and represents that section of the city, has said she opposes building a prison in the District. Rolark testified recently before Specter's D.C. Appropriations subcommittee that the city should pursue alternatives, including prisoner diversion programs, halfway houses and stepped-up job training.

Specter conferred briefly with Mayor Marion Barry this week, and one of the senator's top aides, Tim Leeth, has been working with D.C. Department of Corrections officials for the past two weeks examining possible prison sites.

"The mayor is looking at some sites," Specter said. "We should have some possibilities in a couple of weeks . . . . We have to make a determination as to how big a prison is necessary, and that's a fairly difficult matter."

Specter said "it's entirely possible" that Congress will add money to the District's 1986 budget to finance the preliminary planning of a new prison -- a project that has the backing of Specter, the mayor, U.S. Attorney Joseph diGenova and Attorney General Edwin Meese III.

The City Council is expected to complete work on the city's 1986 budget by the end of March, subject to review by the mayor. Congress will begin hearings on the budget in May.

"I would assume that before the [1986] federal budget goes forward, we will be discussing how to proceed [on a new prison]," said D.C. Budget Director Betsy Reveal. "It's all now on the plate for discussion."

The long-running debate over ways of dealing with D.C. prison overcrowding took a major turn March 5 when Barry publicly endorsed the federally financed construction of a new prison in the District.

In abandoning his opposition to a new prison, the mayor cited an alarming three-month increase in the inmate population that had left the Lorton Reformatory complex in southern Fairfax County and the D.C. Jail, near Robert F. Kennedy Memorial Stadium, bursting at the seams.

The D.C. Coalition for Justice, which opposes prison construction, estimates that it would cost the federal government about $22.5 million to construct a 500-unit prison in the District -- or about $45,000 per bed.

The District government would spend an estimated $22.5 million -- an average of $15,000 per prisoner -- in operating costs during the first three years of the prison's operation, according to the group, which is affiliated with the American Civil Liberties Union (ACLU).

Despite the near-unanimity among top federal and District officials about the need for a new prison in the District, there is much to be done before a final decision can be made on whether to go ahead with the project, officials agree.

Along with selecting a site, federal and District officials must decide whether to build a minimum- or maximum-security facility and agree on long-term projections of crime trends, sentencing and parole patterns and the size and probable makeup of the prison population.

One point that is clear, though, is that a new D.C. prison will be designed to handle the overflow from the seven correctional institutions at Lorton, rather than serve as a replacement facility.

For years, Northern Virginia officials and residents have complained about the 3,500-bed Lorton Reformatory and have urged the District to consider phasing out that facility. However, Barry said recently that the city intends to continue operating Lorton for the foreseeable future.