"Joe and Keira are looking forward to working together again immensely," a friend of the director told the Telegraph.
"I have two actresses as potential Elizas -- one British, the other American," Cameron Mackintosh, who is producing the film with Duncan Kenworthy, told the paper over the summer. The other actress is said to have been Scarlett Johansson.
Last week, Kenworthy said: "I think Keira would be absolutely fabulous in it." Emma Thompson is writing the script for the film, for which Daniel Craig has been pegged as a possible Professor Henry Higgins.
Wright had been due to direct Indian Summer, a film about the relationship between Countess Mountbatten of Burma and Jawaharlal Nehru. Variety reported last week that Universal had put that film on hold.