As Mayor Walter E. Washington moves closer to a decision on whether to seek re-election next year, he faces a racially sensitive and politically thorny prospect - replacement of his fire chief and police chief, both of whom may retire sometime in 1978.

Fire Chief Burton W. Johnson, who turned 60 Sept. 5, says he is "anticipating" retirement and has even discussed a specific retirement date with the mayor, although neither he nor the mayor would say what that date is.

Police Chief Maurice J. Cullinance, who will be 45 on Nov. 29, denies current rumors that he plans to quit soon, but repeated in an interview this week that he does "not want to set any longevity records" as police chief.

D.C. personnel officials said yesterday neither Johnson nor Cullinance has filed retirement papers. A 60-day notice of intention to retire is required for optional (non-medical disability) retirement.

If either or both do formally announce retirement before the Democratic primary election here next September, their replacement are certain to become a hot campaign issue with the mayor coming under heavy pressure to appoint blacks and require them to live in the city.

City hall observers agree race is an unavoidable consideration in replacing Cullinance who is white, and Johnson, who is black. The issue is further complicated by the fact that there are relatively few blacks to choose from in the hierarchy of either department.

Selection of a new police chief became a controversial campaign issue in 1974 when Jerry V. Wilson retired in the midst of the city's new home rule election campaign and lawyer Clifford Alexander, Washington's principal Democratic challenger, called for appointment of a black chief.

Washington ultimately selected Cullinane over several black candidates but not until December, 1974, well after the election.

Many fire and police department officials see a similar controversy sharping up next year. One common scenario has the mayor replacing Cullinane with Assistant Police Chief Burtell M. Jefferson, who is black, and is relatively popular, with the rank-and-file police force and is known to be close to both Cullinane and the mayor. Jefferson's appointment would remove some of the pressure to replace Johnson with a black in the fire department where there are fewer high ranking blacks and no heir apparent as in the police department.

The 4,100-member police force is about 40 per cent black. The 1,450-man fire department is about 30 per cent black. The population of the city is about 73 per cent black.

Mayor Washington asked if he had urged Johnson to stay on through next year to avoid the political problem of replacing him during the election campaign, said through a spokeswoman yesterday. "You better ask the chief about that."

Johnson denies being under such pressure. Cullinane also says he has had no pressure from the mayor to stay on.

Johnson, a widower whose wife was a D.C. police officer, will complete 35 years in the fire department on Jan. 16, 1978. He became the first black fire chief in the city when Washington appointed him on April 23, 1973.

He had been the department's fire marshall just before the appointment, a position equivalent to deputy chief.

There are two assistant chiefs, six deputy chiefs and 32 battalion chiefs in the fire department, all of them eligible to succeed Johnson. One of the assistant chiefs, Jefferson W. Lewis, is black but is not considered a mayor candidate for Johnson's spot by department officials. One of the six deputy chiefs is also blacks as are four of the 32 battalion chiefs.

Unlike the Police Department where there is general private agreement among officials that Burtell Jefferson will succeed Cullinane, the Fire Department has no leading contender. One Personnel Department official said Mayor Washington may even extend his search for a new fire chief beyond the city.

Cullinane was appointed police chief in December, 1974. At 44, he is still young enough to retire and enter a second career. But he said this week he has no specific plans and is not actively seeking another job.

He said speculation about his possible retirement was probably triggered by his periodic visits to the fire and police clinic, often a tip-off that an official is getting ready to quit. He said, however, that he goes to the clinic because of recurrent problems with his left knee which was broken by a brick thrown at him during an antiwar demonstration in 1969.