The board of trustees of the University of the District of Columbia has reached an agreement with Robert L. Green, dean of urban studies at Michigan State University, to become the next UDC president, a board member said yesterday.

Trustee Marjorie H. Parker, a former chairman of the board, said the trustees could vote as early as tomorrow night on Green's appointment, and that it appears certain.

Green would replace Benjamin H. Alexander, who resigned last month after a year on the job.

Alexander said he could no longer run the university in the face of opposition from a majority of the trustees and the faculty leadership.

Ronald H. Brown, board chairman, would not confirm that Green, 49, was the board's choice. But he said he hopes to be able to place a vote on the presidential appointment on the agenda of tomorrow's meeting.

"I fully expect the vote, whenever it is taken, to be unanimous. I don't expect any division between those board members who supported the former president and those who opposed him," Brown said.

The board had been split 6 to 7 over the Alexander appointment. Later the number of Alexander supporters on the board dwindled to only three.

Green, who could not be reached for comment yesterday, was in the city this week conferring with UDC officials and faculty members.

In marked contrast to the controversy that shrouded the Alexander appointment from the start, the possibility of Green's appointment won praise yesterday from a variety of university officials.

"He appeared to be very strong and straightforward, a good strong administrator," said Claude Ford, UDC's vice president for administration, who has served as the acting president for the past month.

"I think he's a fine person who has a good understanding of the higher education system," said Wilmer Johnson, president of the Faculty Senate and one of Alexander's strongest critics. "I believe he has a feel for what it takes to move UDC"

Trustee Terry B. Thomas, one of Alexander's staunchest supporters, also praised Green's past record, and said that Green's educational philosophy stresses academic standards and is similar to that which Alexander expoused. Thomas said he expects that Green will support the policy of placing students on probation who do not maintain an adequate grade-point average, as Alexander had.

"I feel with Green's educational philosophy, he's capable of doing the job," Thomas added. "However, he has never been a university president, so I don't know how successful he'll be in this environment. I can only speculate."

Green, a professor of educational psychology, had been the first choice of the presidential search committee that last year eventually recommended Alexander for appointment after Green turned down the job. In the 1960s, he served as an educational consultant to the Southern Christian Leadership Conference and a close associate of the late Martin Luther King. He is considered an expert in the area of school desegregation. He has been a dean at Michigan State since 1973.