Mayor-elect Marion Barry is expected today to name Elijah B. Rogers, a 39-year-old graduate of Howard University and currently city manager in Berkeley, Calif., as the next city administrator of the District of Columbia, according to knowledgeable sources.

Barry is also scheduled to announce, the sources said, that Robert L. Moore, 38, a one-time southern civil rights activist who is executive director of the Housing Authority of the City of Houston, will replace Lorenzo W. Jacobs Jr. as director of the D.C. Department of Housing and Community Development.

As part of a reorganization of the mayor's officer staff, Barry also is expected to name 44-year-old Gladys W. Mack, the city's acting budget director, to one of five newly-created posts as assistant city administrator. Mack will be in charge of budget operations, sources said.

The names of the other four assistants to the city administrator -- the number tow post in city government -- were not immediately available. There were reports, however, that those under strong consideration included the following:

James O. Gibson, an urban planner at Potomac Institute and longtime Barry intimate, as assistant city administrator for planning.

Judith Rogers, special assistant to Mayor Walter E. Washington, as assistant city administrator for intergovernmental relations.

Barry also is expected to appoint Dwight S. Cropp, executive secretary of the D.C. Board of Education, as expecutive secretary to the mayor, replacing Martin K. Schaller, the sources said. George R. Harrod is expected to, in effect, be reappointed as director of personnel.

The appointments will be the first announced by the mayor-elect, who said several weeks ago that the hoped to appoint at least four top assistants before his Jan. 2 inauguration.

Three of those fur choices -- budget and housing directors and city administrator -- are included in the announcements expected today. The fourth, corporation counsel, is not expected to be made until later, according to the sources.

Florence Tate, Barry's press secretary, refused to comment on the names given by the sources. Barry, chief adviser Ivanhoe Donaldson and transition director Delano E. Lewis were unavailable for comment.

Mayor Warren Widener of Berkeley, where Rogers has been city manager since 1976 said he had not been notified by Rogers of any intention to come to the District of Columbia.

"I know they have been courting him," Widener said in a telephone interview. "I have no indication that he would accept the offer."

Widener said Rogers, a former assistant city manager of Richmond, Va., was a good administrator and also possessed "a good sense for economizing. He also has a good political sense for an administrator in knowing how to keep from causing political flaps."

Reuben W. Askanase, chairman of the board of the Houston housing authority, said he had not been told of any intention by Moore to leave the position Moore has held since Feb. 8, 1976.

"I'd do everything I could to keep him here," Askanase said. "Under him, we've done some of the most unusual things in the country. We've gone to the private sector, we haven't relied on public funds."

Moore grew up in Camden, N.J., was once a special assistant to Housing and Urban Development Secretary Floyd Hyde and ran his own consulting firm.

In keeping with privat pledges by Barry advisers to bring more blacks into the top posts of the new administration, all of those persons mentioned by the sources as expected appointees are black.

Barry has also said that he would look for persons with previous experience in government, some from outside the city and some from within.