The X-Files star is in negotiations to play Miss Havisham in the Charles Dickens drama, The Wrap says.
Ray Winstone and Douglas Booth have already signed up to star in the three-part series, which has been penned by Oliver Twist scribe Sarah Phelps.
Anderson previously appeared in the BBC's 2005 adaptation of Dickens's novel Bleak House.
More recently, she starred in BBC Two's The Crimson Petal and the White and received a BAFTA nomination for her portrayal of Wallis Simpson in Channel 4's Any Human Heart.
Great Expectations is expected to air on BBC One this Christmas.