Jai Courtney and Boyd Holbrook are reportedly the final two candidates for the part of the resistance fighter who goes back in time and fathers John Connor.
According to Deadline, the Alan Taylor-directed film will be the first part of a two-film arc and finish the story of the human resistance's battle with Skynet.
Holbrook recently appeared in The Host and can next be seen in David Fincher's Gone Girl.
Courtney played John McClane's son in the recent A Good Day to Die Hard and has a role in the forthcoming Young Adult adaptation Divergent.
Reese was portrayed by Michael Biehn in James Cameron's original Terminator and Anton Yelchin in the franchise's last instalment Terminator Salvation.
Terminator: Genesis will see Arnold Schwarzenegger return to the franchise as the eponymous cyborg, while Game of Thrones' Emilia Clarke will play Sarah Connor with Jason Clarke as John Connor.
The movie will open in cinemas on July 1, 2015.