It was confirmed on Friday that Cumberbatch will play the WikiLeaks founder in the drama, which is to be directed by Twilight: Breaking Dawn's Bill Condon.
Variety reports that McAvoy is in talks to play Assange's (now former) right-hand man Daniel Domscheit-Berg, who wrote the book – Inside WikiLeaks: My Time With Julian Assange at the World's Most Dangerous Website – upon which the script is partially based.
Former The West Wing and Fringe writer Josh Singer penned the script, which is also partially adapted from David Leigh and Luke Harding's book WikiLeaks: Inside Julian Assange's War on Secrecy.
RoboCop star Joel Kinnaman was previously rumoured to be in talks for the role of Domscheit-Berg, while Jeremy Renner was at one stage interested in playing Assange.
The DreamWorks-produced film is expected to go into production next year.
Watch Benedict Cumberbatch speaking to Digital Spy about Sherlock below: