According to the Daily Mail, Cumberbatch will begin performances in August 2015. Producer Sonia Friedman confirmed that the creatives are in final negotiations with London's Barbican Theatre.
Cumberbatch received the Olivier alongside Jonny Lee Miller for their alternating portrayals of Victor Frankenstein and the Creature in Danny Boyle's Frankenstein.
Lyndsey Turner is slated to direct Hamlet, which will be the centerpiece of Barbican's 2015 season.
Cumberbatch, who has committed to a 12-week run at the Barbican, is known as the star of BBC-TV's "Sherlock" and his performances in "Star Trek Into Darkness" and "12 Years A Slave," among others.