The 23-year-old former model, whose father is "Miami Vice" legend Don Johnson, is currently a 'serious contender' to play the book's heroine Anastasia Steele, reported Contactmusic.
A host of famous faces, including Emma Watson, Kate Beckinsale and Alexis Bledel, have reportedly been considered for the coveted part, but Johnson is said to be a favourite as she has few film credits to her name.
British moviemaker Sam Taylor-Johnson has signed up to direct the Hollywood version of the erotic literary sensation by EL James, while 'Sons of Anarchy' star Charlie Hunnam is the latest name linked to the role of masochistic billionaire Christian Grey.