The TV presenter has reportedly sent two letters to Mills requesting permission to film her.
Theroux told The Sun: "She’d be fascinating. She needs to show her side of the story which, for one reason or another, isn’t coming through. I haven’t heard back so far."
Mills was criticised last year for the comments she made during an interview with GMTV, in which she spoke out about her divorce from Paul McCartney and her treatment by the media.