The book was one of the biggest publishing hits of last year, topping the New York Times Bestseller list and selling over 2 million copies in 2012, reported Digital Spy online.
Producers want Blunt for the lead role of a screen adaptation, with the actress reportedly being perceived to be more appropriate for the lead role than Reese Witherspoon.
Witherspoon was initially linked to star in the film after it was confirmed that she will produce.
The novel tells the story of a man who comes home to discover his wife has disappeared - the story then alternates between the perspectives of the husband and the missing wife herself.
Other names linked with the role include Charlize Theron and Rachel McAdams, with Jon Hamm, Ryan Gosling and Michael Fassbender in contention for the role of the husband.
The screenplay will be adapted by Gillian Welch from her own novel. The screen rights were subject to a studio bidding war, before eventually being sold to 20th Century Fox for 900,000 pounds.
