The Zero Dark Thirty star is up for the role of John Connor, the leader of the resistance army battling to defeat the robotic Terminators, according to Deadline.com.
The character was first referred to in the original film in 1984 and, in 1991, Edward Furlong took on the role.
The news comes a week after movie studio bosses at Paramount announced a Tv series is being developed in conjunction with the new movie.
In addition to the reports surrounding Clarke's casting, actresses Brie Larson and Emilia Clarke have emerged as the front runners to play Connor's mother Sarah.
Terminator: Genesis, which will also feature Arnold Schwarzenegger as the title character, is set to hit theatres in July, 2015.