Alexander Skarsgard is to co-star in the film, which is expected to shoot in South Africa.
"[Producer] Harvey [Weinstein] introduced Taylor to Brenton in Toronto because they were both going to be in the film," a source told the Post, referring to the Toronto International Film festival, which both Swift and Thwaites attended.
Swift, 23, is a country music star whose previous acting credits include "The Lorax" and "Valentine's Day."
Notable deaths of 2014 [PHOTOS]
Jason Aldean to extend Burn It Down Tour