The Defense Department is seeking $2.5 million to demolish the Pentagon's massive south parking lot in anticipation of building a new federal office complex nearby.

If approved by Congress, the project would eliminate 3,782 of the Pentagon's 8,769 parking spaces and create what one Arlington County official described yesterday as serious problems. The demolition funds are being requested as part of the Defense Department's fiscal 1987 military construction program.

Parking at the Pentagon is tightly controlled and most spaces are restricted to car pools. As a result, demolition of the south lot would affect far more workers than the number of parking spaces suggests.

"It is planned that alternative arrangements will be made for employe parking on a temporary basis as the construction program progresses," said Defense Department spokesman Glenn Flood. He said, however, that no decisions have been made on what sites might be used instead of the south lot and, eventually, the other smaller parking lots that may be eliminated for the additional buildings.

Arlington County Board Chairman Mary Margaret Whipple, who attended a briefing on the issue yesterday, said it may lead to "serious problems," and added: "Hopefully, a significant percentage of those people who lose parking will use Metro."

Noting that the few residential neighborhoods near the Pentagon require special parking permits, she warned that the county would enforce that system "to keep residential streets from being overcome by parking."

Whipple said it has been estimated that 18,500 people may work in the new office complex, and said she hoped the Pentagon would develop plans for satellite parking lots and provide additional incentives to use the subway system and car pools.

The Pentagon, with 24,000 workers, is the Washington area's largest office building.

Although construction of the new federal office complex may be years away, Flood said the money was being requested for the next fiscal year "because we need to plan for these things."

The General Services Administration, the federal government's landlord, last May began a year-long study of building a new office complex on the 700 acres of federal land surrounding the Pentagon. Because the study is not expected to be completed until midsummer, no decisions have been made on the height, density or number of buildings in any future office development.

GSA has said, however, that it may be possible to build 3 million square feet of new office space on the federal land bounded by Shirley Highway (I-395), Washington Boulevard, Boundary Channel Drive and Army-Navy Drive. Defense officials have complained that the 43-year-old Pentagon has become increasingly cramped.

Defense Department spokesman Flood said the department expects to replace some of the demolished parking spaces in the south lot with underground lots in any new office complex.

GSA spokesman Dale Bruce said the agency's study on the new complex will examine transportation and environmental concerns.

Whipple said that, in addition to the extra traffic such a development would bring, the new Pentagon buildings would place an additional burden on Arlington's sewage treatment facilities.