The Columbia Pictures project, which Keira Knightley is circling, is a remake of the 1964 movie musical starring Audrey Hepburn as Cockney flower girl-turned socialite Eliza Doolittle. In turn, the film was adapted from George Bernard Shaw's play Pygmalion.
Thompson told Parade that writing the film will take a long time because she does not use a word processor.
"I'm a Luddite, and I write longhand with an old fountain pen," she said.
Thompson is the only person to have won Oscars for both acting (1992's Howard's End) and screenwriting (1995's Sense And Sensibility).