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The Sherlock Holmes actor could be set to star opposite Keira Knightley, who has now signed up for the title role, Variety reports.
It not yet known whether Law would take on the role of the cold, emotionally distant husband or the exciting suitor who distracts Anna from a life of domestic boredom.
Kick-Ass's Aaron Johnson is also currently negotiating a leading role in the period film and could play either role.
Joe Wright has previously directed adaptations Pride and Prejudice and Atonement, also starring Knightley.
Oscar-winning playwright Tom Stoppard, who wrote Shakespeare in Love will script the latest film version of tragic romance Anna Karenina.
It was previously brought to the big screen in 1935 and 1997, starring Vivien Leigh and Sophie Marceau opposite Sean Bean respectively.
Law is also rumoured to be interested in starring in yet another screen adaptation of Dracula.
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