Fund raising for a proposed $4 million memorial to black Revolutionary War patriots will begin soon since President Reagan has approved placing the monument in the city's main tourist district. Project coordinator Maurice A. Barboza said the memorial would be the first prominently displayed monument in Washington dedicated to blacks. Barboza said Monday that the president signed legislation Friday permitting the proposed memorial to the 5,000 black veterans to be placed in Area I, which includes the Mall stretching from the Capitol to the Lincoln Memorial, the grassy Ellipse behind the White House, Lafayette Park and West Potomac Park. The next step will be to study specific site plans being developed by three architectural firms and submitting the best one to the National Capital Memorial Commission, Barboza said. The commission and other agencies must recommend a site before it goes to the Secretary of Interior for final approval. Barboza, a Virginia lawyer who has devoted himself full-time to the memorial project, said he hoped to have the Interior Department approval and start work on a design competition in six months. Construction of the memorial must begin by the end of 1991 under an authorizing measure signed into law in late 1986. Barboza said July 4, 1991, is the target date for construction to begin. Barboza predicted the memorial would cost about $4 million and said he hoped to announce a major fund-raising effort within several months. Barboza said he hopes to built the black patriots memorial on the Mall near the Lincoln Memorial, Washington Monument and Constitution Gardens. Legislation allowing the construction of the memorial was enacted in 1986, but another measure was needed to allow it to be built in the city's monument-crowded Area I. That complex procedure was established by officials who worried that the city's prime tourist areas would become cluttered with memorials. The black patriots legislation was pushed through Congress by Rep. Nancy L. Johnson, R-Conn., whom Barboza enlisted in his fight several years ago. He is formerly of Plainville, Conn., in Mrs. Johnson's district.