City administrator Elijah B. Rogers, who came to Washington 23 months ago as one of Mayor Marion Barry's highly touted "can-do" administrators, is considering leaving the D. C. government.

Rogers, 41, a symbol of progress toward Barry's campaign promise to professionalize the city government, is quietly under consideration for the better-paying and more powerful job of city manager of Oakland, Calif.

"I understand that people have mentioned my name for the job," said Rogers. "That's one of the best city manager jobs in the country. If I'm contacted, obviously I will talk to people."

Oakland officials and Rogers deny that he has been contacted about the job, although they admit that Rogers, one of the few black administrators of a major American city, is being mentioned for the position in predominatly black Oakland. The city has never had a black manager.

Rogers, moreover, freely admits he misses the Bay area, where he once lived for five years.

Rogers' departure, however, would be a further blow to Barry's administration, which already has lost Department of Employment Services chief Wiliam R. Ford and several other high-level administratiors.

But Barry said yesterdy that "no administration expects to keep all its people for four years." He predicted there might be even more turnover in the administration's top ranks before his first term ends in 1982.

"Not everbody makes a four-year commitment when they come on board," Barry said. "Bill Ford only made a commitment for two years, for example. But you don't tell people that it's just for two years, because then it's impossible to get people fired up."

Rogers, who currently is paid $53,000 a year, said the Oakland job now pays $654,000 anually. "That is an area that sooner or later has to be addressed," Rogers said of his lower salary.

He also said the Oakland city manager's job is powerful, with more responsibility and authority than D. C. city administrator job. He said he has "an awful lot of friends" in Oakland.

"Sooner or later, everybody's got to think about the future," Rogers said.

However, he said his "inclination" is to stay in his current job at least until the end of 1982. The Oakland job will become vacant June 1.

Rogers is nominally the second-ranking official in city government. But sources have frequently said that in fact that role was often filled by Ivanhoe Donaldson, Barry's general assistant and chief political aide. The sources described Rogers as dissatisfied with the arrangement.

"I'm 41 years old," Rogers said yesterday. "I'm a big boy now. I know my way around, I know you move up and you move down in a job."

But he added, "I have never had any doubt as to my relationship or authority with tha mayor. I've never had any problem with Ivanhoe trying to usurp anything from me. Nobody rolls over me."

Still, the diminutive, flamboyant Rogers -- who frequently wears shirts with cuffs monogrammed "Baby," his middle name -- has assumed a much more visable role since Donaldson took over as acting director of the employment services department several months ago.

Rogers has become the administration's principal spokesman on financial matters, and has delivered the administration's position on a range of other government issues about which Barry has chosen not to comment, such as the recent decision to place on administrative leave two officials who were found to be subjects of a federal grand jury probe.