Eastwood's son for 50 Shades role?
A source said: "He is one of five actors being considered."
Scott, 27, fuelled the rumours by tweeting: "What is all this talk about 50 shades of grey?? What do you all think?? Let me know. #hype #eastwoodlivin."
The actor made his debut in his dad's film Flags Of Our Fathers in 2006.
Colin Farrell has brushed off any interest in the role. The Irish star, who had been linked to the part, denied he would like to play Christian at the world premiere of Saving Mr Banks, saying: "No. I think that ship has sailed."
Sons Of Anarchy actor Charlie was due to star in the eagerly anticipated movie opposite Dakota Johnson as Anastasia Steele but dropped out earlier this month, citing his busy schedule for his exit. It was later reported that there had also been "creative conflicts" over the script.
The movie version of author EL James' erotic best-seller will be directed by Sam Taylor-Johnson.