Based on a Tony and Pulitzer Prize-winning play, the film will star Julia Roberts alongside Meryl Streep, who plays the matriarch of a dysfunctional family.
Cumberbatch is in negotiations to play the sensitive son of Streep's sister in the film, according to The Hollywood Reporter.
Teen actress Abigail Breslin also recently signed on for a role in the film, which is being produced by George Clooney.
Cumberbatch, best known in Hollywood for his Emmy-nominated show Sherlock, will soon appear in BBC drama Parade's End, in addition to the Star Trek sequel and The Hobbit.
He has just finished production on Steve McQueen's upcoming drama Twelve Years a Slave.