D.C. City Administrator Thomas M. Downs, who has managed the day-to-day operations of the District government for nearly five years, is resigning to take a top transit job in New York City, according to District government sources.

Downs is to become president of the Triborough Bridge and Tunnel Authority, a $200-million-a-year arm of New York State's Mass Transit Authority, according to the sources who said the official announcement may be made as early as today. The appointment to the authority, which manages seven bridges and two tunnels, is subject to the approval of the MTA board.

Downs, who was a finalist last month for a major transit post in Pennsylvania, has long been expected to leave the District government. There is no clear successor to Downs, who is being pressed to remain until Mayor Marion Barry presents the city's fiscal 1989 budget at the end of January.

Downs' departure adds to a list of major vacancies confronting Barry. The mayor, concerned about sagging morale and an image of disarray in his administration, is preparing a staff shakeup that could involve several top jobs, but few firm decisions have been made, according to sources.

Effi Barry, the wife of the mayor and a member of his Cabinet, made an offhand remark to some reporters yesterday that some type of administration announcement would be forthcoming on Friday, but she gave no details of the subject matter.

In addition to Downs' post, Barry is looking for a new staff director, a controller in the mayor's office, a director of finance and revenue and other senior positions. The post of deputy mayor for finance has been left unfilled since March 1986.

Sources said Barry also is planning to reassign or seek the resignation of Sallie Melendez, a special assistant who generated controversy after she was unexpectedly hired away from a public relations job in Oakland to work for Barry at an annual salary of $63,185.

Melendez spent more than seven weeks on the job before she was given any specific duties.

Downs, a former executive director of the federal Urban Mass Transit Administration and director of the District's old Department of Transportation, became city administrator and deputy mayor for operations in May 1983 after former city administrator Elijah B. Rogers left to go into private business.

Downs has played a central role in grappling with many of the Barry adminstration's toughest problems over the last year, including emergency ambulance service, snow removal and the continuing problems with the city's corrections department.

District Building regulars speculated yesterday that Carol B. Thompson, now deputy mayor for economic development and Barry's former chief of staff, may move to Downs' job.

However, some officials said Thompson's deliberate style may be unsuited to the often crisis-like atmosphere of the city administrator's post.