The actor-model sparked the casting report on Twitter, writing, "What is all this talk about Fifty Shades of Grey? What do you all think?? Let me know."
And then a source close to the 27-year-old fuelled the rumour by saying, "He is one of five actors being considered", reported Contactmusic.
The other candidates for the coveted role are Francois Arnaud, Billy Magnussen, Luke Bracey, Jamie Dornan, Theo James and Christian Cooke. The chosen one will play opposite Dakota Johnson, who is tapped as Anastasia Steele.
Eastwood is currently filming David Ayer's World War II action drama "Fury" with the likes of Brad Pitt, Shia LaBeouf and Logan Lerman. He once appeared in his father's 2008 "Gran Torino" and 2009 "Invictus".