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According to the Los Angeles Times, Marvel Studios offered Blunt the role of Peggy Carter, the Captain's girlfriend.
However, the Young Victoria star passed on the offer in favour of other projects.
Other actresses on the studio's shortlist for the part include Keira Knightley and Alice Eve.
Gossip Girl's Sebastian Stan has been cast in the role of sidekick Bucky Barnes in the superhero film.
Filming is due to begin in the summer.
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