The Hollywood Reporter said Friday the untitled movie project would follow Graham's life with the newspaper, including her time as publisher during the Watergate scandal, which began with a break-in at the Democratic National Committee headquarters in 1972 and ended with the resignation of U.S. President Richard Nixon.
Graham became the newspaper's publisher following the 1963 suicide of her husband, Philip. After being honored with a 1998 Pulitzer Prize for her memoir, "Personal History," Graham died in 2001.
The film is being developed by writer Joan Didion and actress Laura Linney is being eyed to take on the role of Graham if it moves forward.
The Reporter said Robert Benton would direct, while Laura Ziskin, Pam Williams and Julie Goldstein will all serve as executive producers.