Although he doesn't give much away, he adds that those behind the film "like the idea" of Greengrass working on the project, although it has not been discussed with Angelina, who is still attached to star as the Egyptian queen.
The movie will be based on the Stacy Schiff biography 'Cleopatra: A Life' and doesn't see the titular queen play the seductress she is known for in Elizabeth Taylor's version of her story, but instead as a smart, tough and political woman.
James Cameron was among the directors who were previously named in contention for the role.
Speaking about the story previously, Scott said: "It is a completely revisionist Cleopatra, a much more grown-up sophisticated version."
Speaking about the role previously, 'Salt' actress Angelina claimed the movie would not see her play a "lovely" version of Cleopatra.
She said: "I will play it differently to Elizabeth Taylor, but I could never be as lovely as she was.
"We are trying to uncover the truth about her as a leader and not just a sex symbol which she really wasn't - she didn't have many lovers, maybe only two, and they're men she had children with."