A Suffolk University trustee said Monday she was blindsided last week when she read in the newspaper that other trustees wanted to oust president Margaret McKenna, while another board member criticized fellow trustees for publicly airing their grievances with the president.

The comments were the latest in an unusually public standoff between some trustees and McKenna, and indicate there could be some dissension among the 28-member governing board.

“For some reason the rest of us are being kept out,’’ trustee Jennifer Nassour said.

Nassour, in a brief phone call, said all she has been told is that trustees plan to meet Friday. It is too soon to decide whether McKenna should be fired after just seven months as president, she said.

“She’s only been in a couple of months so I think it takes more than a couple of months to know what someone’s aptitude is,’’ said Nassour, the former chairwoman of the state Republican party.

Another trustee, John J. McDonnell, also spoke publicly for the first time Monday, saying board members should be communicating behind closed doors, not in the press.

“I run a business,’’ said McDonnell, who is the managing director for Tito’s Vodka. “When I have a potential conflict, I don’t play it out on TV. I’ve never seen anything like this.’’

The spat between some board members and McKenna boiled over Thursday when trustee Mark E. Sullivan suggested privately to McKenna that she depart because chairman Andrew Meyer had enough votes to fire her and potentially hire former state attorney general Martha Coakley.

Meyer, as well as four other trustees, have said McKenna’s style is abrasive and that she has endangered the school’s financial health (and bond ratings) through unauthorized spending. The president has disputed the allegations and declined to resign.

In other developments Monday: Meyer met with student government leaders to address their concerns with the board’s leadership; Coakley, through a spokesman, said she will not comment on the situation; and faculty pointed to a 2014 letter from the school’s accreditors that asked trustees to stop managing daily university business.

Other members of the board, when contacted Monday, did not return calls or declined comment. In response to the comments from Nassour and McDonnell, Meyer said by phone that there was no “plan’’ that could have been communicated to the other trustees.

“We were in the process of having discussions,’’ he said.

As the window of time before the trustees convene closes, a number of students, faculty, and alumni have galvanized in support of McKenna.

Students, as well as professors and former and current employees, maintain that, in their experience, the board is too involved in the daily operation of the college. Indeed, the 2014 letter from the regional accrediting agency noted the same concern and told Suffolk it has until 2017 to reform the board’s practices.

The letter, sent to then-president James McCarthy, said Suffolk’s board planned to complete new bylaws in 2014 based on national best practices and also that trustees planned to step back into a more advisory role after a transition period during which they were involved in daily university business.

The accreditation letter from the New England Association of Schools and Colleges noted that the board had become involved in running the school during a period from 2012 to 2014 when there were a number of new senior administrators.

Accreditors told the school they expected to be assured in an interim report due in the fall of 2017 “that clear lines of authority, responsibilities, and relationships among the board, the administration, and the faculty have been established to ensure an effective governance structure’’ and said the board recognized its need to “return to a more appropriate oversight and advisory role now that the new senior leadership team is in place.’’

Meyer said Monday the new bylaws are drafted but not adopted, and that the process is overseen by a bylaw committee of the board. He said he believes trustees have successfully stepped back into an advisory role.

“The board is an oversight body,’’ he said.

State attorneys general are charged with overseeing nonprofit boards and charities to ensure that trustees uphold their fiduciary duties. Attorney General Maura Healey said Monday that her office is not investigating Suffolk.

“Disagreements between boards and CEOs are not uncommon and of themselves do not give rise to a claim of breach of that fiduciary duty,’’ Healey’s office said in a statement. “The AG hopes this situation is resolved in the best interest of the students of Suffolk University.’’

Laura Krantz can be reached at laura.krantz@globe.com. Follow her on Twitter @laurakrantz.