The portrait shows the screen siren smiling and her eyelids covered in blue eye shadow. It comes from Warhol's 1960s series of pop culture icons like Jacqueline Kennedy and Marilyn Monroe.
The Journal says Cohen bought the portrait for an undisclosed sum from the estate of a major New York dealer. He declined to comment.
The current Warhol auction record is $71.7 million for "Green Car Crash."