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The Emma actress could join Anne Hathaway and Jim Sturgess in the Focus Features project, directed by Lone Scherfig.
Day centres on two people (Hathaway and Sturgess) who meet during high school graduation in 1998 and begin seeing each other one day every year after that.
Garai is circling the role of a woman Sturgess's character marries in the film.
The movie, based on a novel by UK author David Nicholls, begins production this summer.
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