The search for a president of Washington's new public university has been narrowed to four finalists, including Cleveland L. Dinnard, the head of Washington Technical Institute, according to sources.

Not on the list submitted by a seven-member search committee to the university trustees is Wendell P. Russell, president of Federal City College and D.C. Teachers College. Those two public colleges and the Washington Technical Institute are being merged into the new University of the District of Columbia.

The trustees are expected to pick the president by mid-June so he will be able to take office by August when the administrative merger of the three colleges is scheduled to take place. The new univearsity will have about 13,000 students, 2,200 employees, and an annual budget of $51 million. It is also the focus of a serious dispute among students and faculty of the three present colleges over what its academic standards and major program emphasis should be.

According to sources, the other three men, besides Dennard, on the list of finalists are:

Herman R. Branson, 62, president of Lincoln University, a predominantly black college, near Philadelphia with an enrollment of about 1,000. Branson taught physics at Howard University from 1941 to 1968.

Randolph W. Bromery, 51, the chancellor in charge of the main campus of the University of Massachusetts at Amherst, which has about 20,000 students. Bromery, a geophysicist, worked for the U.S. Geological Survey in Washington from 1948 to 1968.

Walter C. Daniel, 55, the vice-chancellor - second-ranking administrative officer - at the main campus of the University of Missouri in Columbia, with an enrollment of 24,000. Daniel, who also is an English professor specializing in contemporary black literature, came to the university five years ago after serving as president of Lincoln University, a mostly-black college of about 2,000 in Jefferson City, Mo.

Dennard, the youngest of the finalists at age 48, has headed the Technical Institute since it opened nine years ago. He previously had been principal of a large vocational high school in Atlanta and had served briefly as a deputy commissioner for manpower training in the New York City government.

A forceful administrator, Dennard has dominated WTI since it opened, shaping most of its programs and even the design of its buildings. The two-year technical school now has an enrollment of about 4,900.

Although Dennard is highly regarded by the congressmen who deal with D.C. affairs and many local officials, he has drawn sharp criticism from faculty members at both Federal City and WTI who charge that he is high-handed and anti-intellectual.

All four of the finalists for the president's job are black men. However, sources said that whites and women were on the list of 16 from which the finalists were selected after interviews. Overall, the search committee considered 141 names, most of whom applied for the job as a result of advertisements carried in newspapers and magazines nation-wide.

By law, the salary of the university president may not exceed that of Washington's mayor, $52,500, although the exact amount is negotiable.

Russell, who has headed Federal City and D.C. Teachers College since 1974, survived several hurdles in the search committee's elimination process but was not among the four finalists, one source said, because he was not as well regarded as the others.

The search committee, which included four trustees and three other persons named by the board, made its report on May 13. This was at the end of the week in which Russell, despite faculty protests, had allowed two students to graduate from D.C. Teachers College even though they failed required courses in mathematics. A source said Russell had been eliminated by the search committee several weeks earlier.

The four finalists are scheduled to be interviewed by the university's full 17-member board of trustees today and Saturday.