It was recently reported that she's looking for a home in Los Angeles - and it may just be because she has plans to embarked on a Hollywood acting career.
According to the Daily Mirror, the 29-year-old British singer is currently in talks to appear in the upcoming Fifty Shades Of Grey sequel.
The newspaper reports that she recently met with director Sam Taylor-Johnson at Hollywood's Chateau Marmont, where it is said they chatted for 90 minutes about a possible role.
A source said: "They were definitely making some plans. They are friends, and move in the same circles in London, they're in that trendy set. Lily would be the perfect person to work on the next Fifty Shades movie."
However, when contacted by MailOnline, a spokesperson for Allen said that the claims were untrue.
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.
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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