Allen has been in Los Angeles working on her new music, but her profile is thought to be ideally suited to starring in the next movie based on the erotic novels by E.L. James.
The insider added: "She is cool and young, and would bring a new edge to it, especially after all of the rows that have supposedly gone on behind the scenes.
"Lily is an extremely talented and versatile star who would do a fantastic job."
Last week, meanwhile, it was reported Jamie Dornan is "committed" to a Fifty Shades sequel.
Dornan, 32, wants to continue his role as Christian Grey in the erotic film because it "benefits" his family - which includes his wife Amelia and their 15-month-old daughter Dulcie.
Read more:
• Fifty Shades of Grey breaks NZ's R18 record
• Is Jamie Dornan walking away from Fifty Shades?
Following speculation that he would walk away from the racy franchise, a source said: "It's quite the opposite and they (Jamie and Amelia) are both committed to the project because of the benefits to the family."
Should she take on the role, she'd follow in the footsteps of fellow singer Rita Ora, who made a very brief appearance in the hugely successful first movie, which also starred Dakota Johnson.
- Daily Mail