D.C. City Administrator Thomas M. Downs' possible appointment to a major transit post in Philadelphia poses new problems for the Barry administration, which is already hampered by key vacancies and continuing federal investigations.

Downs, who also is deputy mayor for operations, was in Philadelphia yesterday for interviews with the Southeastern Pennsylvania Transit Authority, which is nearing the end of a search for a new general manager. Downs has been in his current job for more than four years and his leaving has been the subject of rumors for months.

A former federal mass transit executive, Downs is one of five finalists to run the transit agency, a $554 million, 9,000-employe authority for the Philadelphia region, according to the Philadelphia Inquirer. Downs could not be reached for comment yesterday.

John C. White, Barry's press secretary, said yesterday Down's possible appointment "is further evidence of the quality of the people we have in the Barry administration."

Downs' willingness to discuss a job in Philadelphia is the first public indication that he is considering resigning. That fact, city officials said, could undermine Downs' authority if he chooses to stay. If he leaves, Barry will be confronted with another major appointment with no clear successor.

"It's the first time the press is able to report . . . he is looking for a job. It's one thing to have a rumor, {but} quite another to have him as a finalist," one District official said. "When subordinates know you're trying to leave . . . they tend to start positioning themselves," for the next appointee, another said.

Downs is responsible for the daily running of the city government and has been key in handling a variety of administrative crises that have hit in the past year, including a major riot at Lorton, snow removal last winter and continuing problems with the ambulance service.

"The mayor would face some difficulty in attracting a top flight administrator . . . with all the probes {and problems} going on, in addition to the other things like pay," a third official said. By law, Downs' salary is limited to $71,000, far below that of many major cities. The Philadelphia post would pay at least $95,000, officials said.

Another ranking District government official said trying to replace Downs now would be like "trying to hire a first mate on the Titanic after it hit the iceberg."

In recent weeks, Barry has been privately criticized by his own aides for his handling of his administration. While the mayor is credited with making several strong appointments at the start of his third term, he has been unable since March 1986 to fill the vacant post of deputy mayor for finance.

Alphonse G. Hill, the former deputy mayor, has pleaded guilty to defrauding the government and is serving a 30-month prison sentence in Allenwood federal prison in Pennsylvania.

In addition, Barry has not found a replacement for Melvin W. Jones, former director of finance and revenue who resigned in August to become a Howard University vice president.

David A. Rivers, a former director of the Department of Human Services who is being investigated by prosecutors probing city contracting, is on leave as secretary of the District.

M. Jerome Woods, Barry's nominee for the massive Department of Human Services, was appointed even though Barry's staff had significant reservations about him, according to one senior official who said the mayor's office settled on Woods just to fill the post.

Downs, who succeeded city administrator Elijah B. Rogers in May 1983, is widely reported by his friends to be burned out. Although credited with excellent administrative skills, Downs has never attained the power that Rogers' had as someone who could always speak for Barry.

"It's a rotten job," an official said, "to be on call 24 hours a day . . . to be awakened in the middle of the night and {someone} say the city's prison at Lorton is burning down."

Downs was mentioned last year as a possible nominee for a transit job in Dallas, but remained with Barry for the start of the mayor's third term with an understanding that he would remain no more than two years, according to knowledgeable District officials.

Of the five Philadelphia finalists, Downs and Theodore Weigle Jr., director of Chicago's regional transit system and a former deputy general manager of Metro in Washington, are considered top contenders, according to a former mass transit official familiar with the search. The other finalists identified by the Inquirer are Charles Thomas and Frank Wilson, staff members of the agency, and William Stead, director of San Francisco's Municipal Railway.