Vincent E. Reed, a federal education official and former D.C. school superintendent, was nominated yesterday by Mayor Marion Barry to fill an unexpired term as a trustee of the University of the District of Columbia.

D.C. Republican Party officials recently expressed interest in trying to coax Reed from his Reagan administration post to challenge Barry, who is up for reelection this year. However, Reed, 53, an assistant secretary in the U.S. Department of Education, rejected that idea last month.

"I don't want to be mayor," Reed told a reporter. "I'm not a politician."

Barry selected Reed from a list of candidates submitted by a nominating committee of the university's Board of Trustees.

If confirmed by the D.C. City Council, Reed would replace Lawrence Brailsford, who resigned. Brailsford's term runs through April 1983.

"Dr. Reed will bring to this position the wealth of experience and leadership capability that he has gained at both the local and national levels throughout his distinguished career," Barry said yesterday, in announcing the nomination.

Trustees serve without salary, but are entitled to per diem payments of up to $4,000 a year, according to an aide to the mayor. They also are reimbursed for expenses incurred while conducting official business.