The play, which was previously seen in London, will be mounted in New York at the Ethel Barrymore Theatre.
Elling, according to the New York daily, tells the story of "two inmates from a mental institution who, under the supervision of a social worker, are given a shot at living on their own." Playwright Bent adapted the work from a 2001 Norwegian film.
O'Hare would play the title role with Fraser as a 40-year-old virgin. Coolidge would play Fraser's girlfriend.
Howard Panter will produce.
Brendan Fraser has been seen on screen in "Gods and Monsters," "Crash," "The Mummy," "Dudley Do-Right" and more.
Denis O'Hare received a 2004 Tony nomination for his work as Charles Guiteau in the Tony-winning revival of Assassins. He won the Tony for his performance in Take Me Out. O'Hare's other Broadway credits include Inherit the Wind, Sweet Charity, Major Barbara, Cabaret and Racing Demon.
Jennifer Coolidge appeared on Broadway in a revival of The Women.
No official announcement about the production has been made.