The Game of Thrones actress impressed Paramount and Skydance executives when she recently read for the iconic part, which was originally played by Linda Hamilton.
Brie Larson and Margot Robbie were also previously being considered for the role, according to Variety.
Alan Taylor (Thor: The Dark World) is slated to direct the new Terminator film, from a script by Laeta Kalogridis and Patrick Lussier.
Little is known about the storyline, other than that Arnold Schwarzenegger is expected to reprise his role from the first trilogy.
It was reported earlier in the week that White House Down star Jason Clarke is in negotiations to play human rebellion leader John Connor.
A companion Terminator television series is also in development to potentially air alongside the movies.
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