Hawke, who recently directed and starred in the Off-Broadway play Clive, is planning to take on the blood-thirsty title role on Broadway at the Vivan Beaumont Theater.
Representatives for Lincoln Center Theater could not confirm the report.
Hawke previously appeared on the Beaumont stage in the Tony-winning production of Tom Stoppard's The Coast of Utopia. He was Tony-nominated for his performance.
Lincoln Center's Beaumont Theater currently hosts the Tony-nominated production of Holland Taylor's one-woman play Ann, which extended through Sept. 1. A subsequent Beaumont production has not been announced.
Hawke was recently part of "Uncovering Shakespeare," a PBS series dedicated to the Bard's work. Hawke took viewers through the world of Macbeth in the episode.
Alan Cumming currently stars in his one-man production of Macbeth, which runs through July 14. Patrick Stewart starred in a Tony-nominated 2008 revival, while Kelsey Grammer took on the role on Broadway in 2000.
Holed up in a seedy motel on the edge of the Mojave Desert, two former lovers unpack the deep secrets and dark desires of their tangled relationship, passionately tearing each other apart. Led by director Daniel Aukin (Back Back Back at MTC, 4,000 Miles), Tony winner Nina Arianda (Venus in Fur at MTC, Born Yesterday) and Sam Rockwell (A Behanding in Spokane, The Way Way Back) bring an explosive intensity to Sam Shepard’s (Buried Child, True West) landmark myth of the new Wild West.