The American University Board of Trustees has agreed to offer former president Richard Berendzen a settlement package of more than $1 million in return for Berendzen's agreement to sever his ties with the university, sources said yesterday.

The settlement, which is not final, was authorized by the trustees at a closed meeting Friday, six months after Berendzen stepped down amid allegations that he had placed obscene telephone calls from his office.

Sources said the board's decision followed an acrimonious debate in which some trustees contended that the payout would be too expensive, while others argued that Berendzen should not be forced to relinquish his AU affiliation.

Since resigning as president, he has technically remained a tenured physics professor, although he has not been teaching or doing other work on campus.

The sources said most board members believed the severance arrangement was in the best interest of the campus in Northwest Washington that was stunned last spring by a scandal involving its high-profile president of 10 years.

"People felt very strongly he should just leave completely," said one board member who attended the meeting. "Just clean the air of the whole distasteful mess."

Reached at home yesterday, Berendzen said, "I really just don't want to get into anything dealing with contracts."

When Berendzen quit in April, he cited exhaustion after a decade-long stint as president that was marked by 100-hour work weeks, intensive fund-raising, and a whirlwind pace on the Washington social circuit.

Later that month, he acknowledged that he had resigned for a different reason: Trustees had learned he was under investigation by Fairfax County police for allegedly placing telephone calls to a woman who ran a day-care service. The woman, Susan Allen, said that in repeated phone calls to her he graphically discussed fantasized sexual relations with children.

He pleaded guilty to two charges of making the telephone calls, and Allen has sued him, seeking $2 million in compensatory damages and $2 million in punitive damages.

He also checked into a sexual disorders clinic at Johns Hopkins Hospital, where he was a patient for 3 1/2 weeks in the spring.

He and his wife, Gail, moved late last summer out of the university-owned president's house. They are now living in a three-bedroom apartment in Crystal City.

Sources said he does not have another full-time job, although they said he has given lectures on astronomy, his professional discipline, and on child abuse. Berendzen would not discuss his activities or his plans. "It's been a very hard time," he said. "I don't think I can say anything more than that."

Since resigning, his exact relation to AU has been ambiguous. He held tenure in the physics department, but he was not teaching and had not sought the required permission for either a sabbatical or an unpaid leave. "His status has not been clear," said Anita Gottlieb, a university spokeswoman.

In the meantime, he has been drawing a salary, although it could not be learned yesterday how much. He was paid about $140,000 a year as president. A campus search committee is screening candidates for a new president, while the school's provost is filling in.

Gottlieb confirmed yesterday that "after January, there will be no continuing relationship with Dr. Berendzen and the university."

Yesterday, Valerie Morris, chairman of the University Senate, said that she had heard rumors of a severance arrangement, but did not know of it firsthand.

Sources said that although the trustees on the 48-member board authorized the settlement, many important details remain unresolved. Lawyers for the university and for Berendzen are negotiating how the payments would be made, their duration, and how they would be classified by a university that has a relatively meager endowment.

The precise dollar amount could not be learned, but one source said the sum "was in the ballpark" of $1 million, and another said the figure exceeded $1 million.

One trustee, Richard S. Cohen, of Potomac, said the package included a buyout of Berendzen's tenure, some funds committed to Berendzen as part of his original contract when he became president and a settlement.

Some trustees argued Friday that the university did not owe a large sum to a president who they said had embarrassed the campus. Cohen responded, "Dr. Berendzen, in my opinion, has made AU what it is today . . . . Enrollment is up, the endowment is up, SATs are up . . . . He is probably entitled to one hell of a lot more than {we} are giving him."

Berendzen referred most questions to his attorney, Richard Marx, who would not confirm the proposed settlement or describe his client's status specifically. "His future plans are indefinite," Marx said. "To the best of my knowledge, there is, as yet, nothing that I would feel comfortable reporting to you about."

Sources said that Berendzen has occasionally met during the last few months with various trustees. One source said he has been trying to work out a settlement, but another said he had conveyed conflicting sentiments about whether he wanted to return as a teacher.

Board sources said that his status was the dominant topic at Friday's regular trustees meeting, and that the three dozen members present debated first whether Berendzen was still entitled to tenure. According to academia's custom, tenure is conferred by faculty committees and provides a strong form of job security that protects faculty members from being fired by administrators.

In Berendzen's case, the trustees disagreed whether he was still eligible for the protection because, as president, he had had an administrator's contract. The majority of trustees contended that he warranted the protection and that they could not fire him.