The Oscar-winning writer behind Little Miss Sunshine was hired to work on the Star Wars Episode 7 storyline months before the announcement that Lucasfilm was to be sold to Disney, according to Vulture.
Arndt has apparently produced a 40 to 50-page extended outline for the upcoming sequel, and is now considered a leading candidate to write the full screenplay.
Meanwhile, Deadline claims that the scribe has also written treatments for two further Star Wars films.
Arndt already has a relationship with the Disney-owned Pixar and has experience writing big franchise movies, having worked on the script for Hunger Games sequel Catching Fire.
Directors linked with the job so far include Matthew Vaughn (Kick-Ass, X-Men: First Class) and Colin Trevorrow (Safety Not Guaranteed).
Lucasfilm founder and Star Wars creator George Lucas has said that he is handing the franchise over to others in order to concentrate on "personal films".
Watch the Blu-ray trailer for Star Wars: The Complete Saga below: