According to Variety, the Academy received three claims on Wednesday, sparking a probe into his behavior.
The investigation comes in the midst of the #MeToo and #TimesUp movements against sexual harassment and inequality.
John Bailey, the president of the Academy of Motion Picture Arts and Sciences, is under investigation for allegations of sexual harassment. If he were forced to step down, he would be temporarily replaced by Lois Burwell, a veteran makeup artist who is the Academy's vice president, until the next election in July.
On Friday the academy said in a statement: "The academy treats any complaints confidentially to protect all parties. We will not comment further on such matters until the full review is completed". The Academy revoked Weinstein's membership after dozens of women came forward accusing him of rape, sexual assault and sexual harassment.
The Academy have released an official statement in response to the allegations..
Governors also may serve on additional Academy committees including: Membership & Administration, Awards & Events, Finance, Museum, Preservation & History, and Education & Outreach.
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Bailey did not respond to CNN's request for comment.
Bailey, 75, who shot films such as The Big Chill, Ordinary People and Groundhog Day, was elected to head the academy last August, three months before reports about Harvey Weinstein's alleged predations triggered a cascade of revelations and allegations about sexual misconduct by other powerful men. His exodus was determined in a vote by Academy members. In December, Bailey established a code of conduct outlining disciplinary action for sexual misconduct or discrimination of any kind.
Bailey told the annual luncheon for Oscar nominees in February that the 90-year- old Academy was reinventing itself with programs committed to inclusion and diversity.
Calls and emails to Hudson and Bailey were not immediately returned.
Though the position of academy president is unpaid and has traditionally been largely ceremonial, in recent years, it has become more demanding and closely scrutinized.