According to the International Business Times, the Harry Potter actress is wanted to play EL James's female protagonist Ana in the erotic movie.
The Twilight-inspired novel follows a young college student as she embarks on a BDSM relationship with an older businessman.
Universal Pictures and Focus Features, who won the rights in March, recently confirmed Mike De Luca and Dana Brunetti as the producers for the film.
Hollywood actresses Emma Roberts, Ashley Benson and Lucy Hale have all expressed an interest in the part of Ana.
Meanwhile, Chris Pine and True Blood's Alexander Skarsgård have been linked to the lead role of Christian Grey.
Angelina Jolie has been named as a potential director of the movie.