The company's board will vote on Hunter's nomination on Thursday, February 10.
"Christine Hunter is one of the Metropolitan Opera's truest and most capable friends," said Met president and CEO William C. Morris in a statement. "She has supplied leadership and invaluable advice to the Met for more than 20 years, and has been active in other opera companies' fundraising and management even before that."
The nomination was first reported by the Washington Post on February 3, and confirmed by Met officials a day later.
Hunter would succeed opera great Beverly Sills, who stepped down last month because of the failing health of her husband and her own broken knee.
"Following in the footsteps of Beverly Sills is an unenviable task," Hunter said. "Beverly brought a unique history and experience to our company, and we are certainly grateful to have had her leadership for as much time as we did."
Hunter is a longtime member of the boards of both the Met and Washington National Opera. She has previously served as president and chair of Washington National Opera, and is currently chair of the Met board's executive committee.
She also runs the Gramma Fisher Foundation, founded by her father, which has supported many opera productions around the country.