According to Twitchfilm, Evans has been offered a role as a villain in the upcoming instalment of the action movie franchise.
Evans is one of several stars recently rumoured to be joining the film, including singer Rihanna.
The actor can be seen starring opposite John Cusack in the crime thriller The Raven, and is presently filming Peter Jackson's The Hobbit with Martin Freeman, Ian McKellen, Richard Armitage, and Aidan Turner in New Zealand.
The Fast and the Furious 6 is scheduled to begin shooting in Europe this June.
Michelle Rodriguez, Vin Diesel, Dwayne Johnson, Jordana Brewster and newcomer Gina Carano are tipped to star in the movie.
Watch the trailer for Fast Five, the previous movie in the Fast and Furious franchise, below: