According to Islands Business, Winston Thompson had been instructed to convene the meeting by the interim council chair, Nauru's president, Lionel Aingimea.
Aingimea told Thompson that the university's supreme body would need to determine his fate and that of the chair of the Council's Audit and Risk committee, Mehmood Khan, also of Fiji.
It reportedly stemmed from the pair's refusal to accept the council's decision earlier this month to clear USP Vice Chancellor Professor Pal Ahluwalia of misconduct allegations.
In June, Ahluwalia was suspended by the USP's executive committee, led by Thompson, over alleged malpractice in a decision that was widely derided as politically motivated.
He was reinstated after weeks of protests by students and staff, when the university council - which includes most of the region's governments - ruled due process had not been followed.
Last week, Thompson said he had accepted the decision by the Council to exonerate Ahluwalia, but claimed that a disconnect remained between the council and the university management.
Since the professor's appointment last year, both Thompson and Khan have led a campaign to remove the Canadian academic.
Aingimea said the meeting to discuss their fate had to take place within the next 10 working days.
Last week Thompson told media that USP lost significant revenue under the leadership of Professor Ahluwalia, and claimed the Vice Chancellor was trying to restructure the institution without following the proper channels.
Earlier, Aingimea criticised a move by Thompson to schedule an Executive Council meeting to review the dismissal of a former university executive
The head of the USP's Pacific Technical and Further Education programme, Hasmukh Lal, was dismissed in May over concerns relating to his academic credentials and the circumstances in which he gained them.
Aingimea said Thompson was undermining the USP Council and its authority.
In a letter to Thompson, President Aingimea accused him of "muddying the process once again".
The Nauru leader said the Lal matter was before the Council and it was awaiting an Executive Committee report to address the issue.
"There are also serious conflicts of interest in discussing the Lal matter if it involves you, the Deputy Pro Chancellor, the Chair of Audit and Risk Committee and the Vice-Chancellor," Aingimea told Mr Thompson.
"These conflicts of interest automatically undermine the credibility of the meeting you are calling."
"Prudence would be the operative word I leave with you and strongly recommend that the Executive Committee meeting be deferred until such time as the issues in the BDO report and the Executive Committee report is submitted to Council and decision taken accordingly."
Senior USP academics and staff had been implicated in the report of manipulating allowances to pay themselves hundreds of thousands of dollars they were not entitled to.
The discrepancies were revealed by Vice-Chancellor Pal Ahluwalia in a 2018 report to the committee.
Ahluwalia's whistle-blowing led to the Auckland office of international accounting firm BDO being brought in to investigate.
Meanwhile, Lal has taken legal action against the university.
In his writ of summons, filed in the Suva High Court in late May, Lal's lawyers claimed the USP failed to afford their client "due process, natural justice and procedural fairness".
Lal also claimed negligence and breach of duty of care in his writ.