Although has revealed the duo are attached to the film, no official deals have been made as the project still has no financing secured.
However, over the coming days Miller looks set to shop the film around Hollywood studios.
What exactly Three Thousand Years of Longing is about remains somewhat a mystery; The Hollywood Reporter notes that the film will be an epic love story involving a genie.
Miller has not directed a film since Mad Max: Fury Road, a project that went through development hell for more than 15 years but was nominated for best picture at the Oscar's upon release.
Meanwhile, Elba has been filming the Fast and Furious spin-off Hobbs and Shaw, playing the villain opposite Dwayne Johnson and Jason Statham. The actor also recently secured a role in the cinematic adaptation of Cats.
Swinton will appear in the horror movie Suspiria later this year, playing two roles; one as a female teaching instructor, one as an ageing male psychiatrist. The actor has multiple projects in the pipeline, including Armando Iannucci's adaptation of The Personal History of David Copperfield and Jim Jarmusch's The Dead Don't Die.
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