Robert L. Green, a prominent civil rights activist and a dean at Michigan State University, has emerged as the leading candidate to replace Benjamin H. Alexander as president of the University of the District of Columbia, well-placed sources at the school said yesterday.

Alexander, a conservative educator with a feisty, outspoken style, who has been president for the past year, announced Saturday that he plans to step down next month because he believes he cannot accomplish the goals he set for the university under continuing opposition from a majority of trustees and some faculty members.

Green currently heads the urban affairs program at Michigan State, recently hit severely by budget cuts. He was the first choice of the UDC presidential search committee that eventually recommended Alexander for the job last year--after Green withdrew his name from consideration, a search committee source said.

Meanwhile, The Washington Post has obtained a copy of a confidential report compiled by Alexander's staff outlining several examples of alleged waste and mismanagement, which it says Alexander has been confronted with since he took over as president last Aug. 1.

The report says:

* Faculty members e giving passing grades to students who did not deserve to pass.

* Some employes were conducting personal business on university time, including one employe who was allegedly running a real estate business from her university office.

* University staff in several departments were permitted to come and go at will without submitting the required forms for sick or annual leave.

* There was no uniform system for evaluating employes' job performance or of training employe supervisors.

* The university was failing to collect substantial funds owed to it from cash advances for employe travel and student loan defaults. And employes were purchasing goods and services without using proper procurement procedures.

Alexander has declined to comment on the report.

Wilmer Johnson, president of the UDC Faculty Senate, said he knew of no instances in which a faculty member has given a student a better grade than was deserved.

He said that faculty members' performance are evaluated annually, and that an evaluation system exists for other employes.

Eugene Harrington, the university's chief personnel officer, said he could not comment on the report without first reading it, but noted that under Alexander, the university established new procedures for evaluating its employes and a new training program for supervisors will be held this summer.

Claude Ford, UDC's vice president for administration, said that in the past, employes had purchased goods and services without using proper procurement procedures, but that the university is currently working to change that.

He said the university did an investigation of the allegation that one of its employes was conducting a real estate business on university time, but that the allegation could not be substantiated.

Ronald H. Brown, chairman of the UDC Board of Trustees, said he had never seen or heard of the report.

Possible Alexander successor Green, who could not be reached for comment yesterday, was a close associate of Martin Luther King, and accompanied him on several of his marches throughout the South. Green later became an educational consultant to the Southern Christian Leadership Conference.

In the late '60, Green, who holds a Ph.D in educational psychology, co-authored a study that concluded that using a "reward system" is an effective way to motivate students to learn.

Brown said the board "has someone in mind" for the job, though he declined to name the candidate and say whether the job had actually been offered. "Suffice it to say, we do not expect to need a long search. We fully expect to have a president in place for the fall semester."

Trustee Terry B. Thomas said he did not know whether Green would be the trustees' ultimate choice, but added, "I understand that Green . . . is seriously considering making a run for it."

Brown said the trustees may make a decision on a possible successor to Alexander as early as next week.

Ford was mentioned yesterday by trustee Joyce Payne as a possible interim successor to Alexander. Ford is second in command in UDC's administration, Payne said.

Trustee Marjorie H. Parker said the board intended to look again at some of the candidates it considered during the last search for a president. The board considered more than 90 candidates during that search, which took nearly two years.