The model is close friends with Aaron Taylor-Johnson, who is married to Fifty Shades director Sam Taylor-Johnson, according to the Daily Mail.
Delevingne has now tried out for a part in Fifty Shades of Grey in a bid to further her acting career and impressed producers with her audition, the reports have claimed.
Details of which role Delevingne attempted to secure have not yet been released, though she is not thought to be hoping to land the lead role of Anastasia Steele.
Meanwhile, some sources have claimed that Delevingne - who met Aaron Taylor-Johnson on the set of Anna Karenina - could have a part written especially for her.
Aaron Taylor-Johnson has previously ruled out a role in the Fifty Shades of Grey movie, saying he is "not Christian Grey".
Photo gallery - 50 Shades of Grey - the rumoured cast: