According to The Hollywood Reporter, the Oscar-nominated actress is in final negotiations for the film, which is based on a true story.
Mulligan would play a widow named Edith Pretty, who has a hunch that her land contains buried riches. The hunch ultimately pays off. Fiennes is Basil Brown, a local archeologist that works with the widow only to see himself pushed aside by museum curators.
The film comes from director Simon Stone ("The Daughter").
Mulligan most recently starred in Paul Dano's drama "Wildlife" and on Broadway in "Girls and Boys."