Bailey, 75, who was elected president of the organization in August, is a cinematographer and occasional director.
Variety reported that the academy, which has a staff of 350 people, opened an investigation on Wednesday upon receiving the complaints.
Saudi threatens to develop nuclear bomb if Iran does
Crown Prince Mohammed bin Salman told United States network CBS News his country did not want to acquire nuclear weapons. Iran agreed to curbs on its nuclear programme as part of a landmark deal reached with world powers in 2015.
The Academy has been largely lauded for its response to the #MeToo movement though, with the group quickly voting to expel Weinstein and Bailey overseeing the establishment of a new code of conduct for the industry.
"The membership committee reviews all complaints brought against academy members according to our Standards of Conduct process, and after completing reviews, reports to the board of governors", the group said in a statement.
Cinematographer John Bailey, 75, is facing three separate harassment claims, USA news outlet Variety claimed.
Tomb Raider Fans Not Happy About Sexist Comments on Alicia Vikander
The ensemble is pretty weak and all of the supporting characters have incredibly one-dimensional motivations that don't hold up. As someone who is admittedly not a huge gamer, I wasn't sure what the movie might have to offer to someone like me.
Upon his election to a four-year term, succeeding Cheryl Boone Isaacs, there were concerns about whether a 75-year-old white man was best suited to lead the Academy at a time when it is making a push to diversify its membership.
Weinstein has been accused of sexual assault by a number of high profile actresses in Hollywood - among them Angelina Jolie, Gwyneth Paltrow, Kate Beckinsale and Lupita Nyong'o - but has denied all accusations of non-consensual behaviour.
Just days after those stories hit the press, the Academy voted to kick out Weinstein - which raised awkward questions about what the organization planned to do about all the other accused predators in its midst.
Federer explains why Novak Djokovic's exit at Indian Wells is 'not surprising'
Federer returned to stadium court on Sunday afternoon and needed an hour to finish off his second round victory 6-3, 7-6 (8-6). Federer saved a set point in the second-set tie-break before easing through.
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. 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.