The project, which has the working title of 1952, is set to be directed by Mission Impossible: Ghost Protocol director Brad Bird.
The Hollywood Reporter now claims that Clooney will appear in the film, which has been described as being close in subject and tone to Steven Spielberg's alien invasion drama Close Encounters of the Third Kind.
The plot is being kept top-secret by the studio and the talent involved - 1952 is understood to be a fake codename, alongside the previously-reported title Tesla.
Clooney's next project is the WWII drama The Monument Men, which he will direct and star in alongside Bill Murray and Daniel Craig.
Lindelof's schedule is equally busy, with new HBO show The Leftovers set to debut next year, and Star Trek Into Darkness, which he is producing and writing, arriving in cinemas in May 2013.