Edward J. Derwinski, a 24-year Illinois congressman who moved to Foggy Bottom in 1986, acknowledged yesterday that he's interested in the job of postmaster general. The current head of the Postal Service, Preston R. Tisch, recently announced plans to resign, but will stay on until the service's Board of Governors names a replacement.

Derwinski, the undersecretary of state for security assistance, science and technology, served on the House post office panel while a member of Congress. "Yes," he said, "I would be interested if the Board of Governers is interested in talking to me.

"I'm not out twisting arms, but I am in the position of a bashful girl that's willing to say yes," he said.

The next postmaster general is not expected to have an easy ride, since the post office faces $430 million in budget cuts during the next 21 months. A spokesman for the postal governors did not return calls yesterday.

Bergquist: Time's Up . . .

Kenneth P. Bergquist, selected by President Reagan last year to become the Pentagon's chief of Special Operations Forces, has withdrawn his name from consideration.

Bergquist, a friend of Defense Secretary Frank C. Carlucci, is a deputy assistant attorney general at the Justice Department's Office of Legislative Affairs.

"It took me six months even to get a hearing," Bergquist told the Associated Press, referring to a Senate confirmation hearing last month that ended without a vote. "And I didn't see any prospect of getting a vote anytime soon. I think I would have won a vote, but I had no guarantee of getting one. So it didn't seem prudent to keep going."

McAllister for State . . .

The White House announced yesterday that the president will nominate Eugene J. McAllister to succeed Douglas W. McMinn as assistant secretary of state for economic and business affairs. McAllister, a former Heritage Foundation fellow, has been on the White House staff since 1983.

C. Christopher Cox, senior associate White House counsel, has announced his intention to run for the southern California seat being vacated by Republican Rep. Robert E. Badham. The third-ranking lawyer in the White House counsel's office, Cox practiced law in Newport Beach, Calif., as a partner at Latham & Watkins before joining the administration in 1986. Cox joins several local Republicans in seeking the GOP nomination in the June 7 primary.

Brock's Directorship . . .

Burson-Marsteller in New York has elected Dole campaign chief William E. Brock as a company director. Rejoining the public affairs firm here is Lance Morgan, who took a 10-month leave to work as press officer for the Senate select committee on the Iran-contra affair.

Cassandra Moore has been named executive director of the newly formed interagency council on the homeless by HUD Secretary Samuel Pierce. Until recently, Moore was director of urban affairs at the National Association of Realtors. This makes her a member of Washington's latest "power couple." Her husband is Thomas Gale Moore, a member of the Council of Economic Advisers.