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.
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.