Arndt has already spent months writing a 40-to 50-page treatment for the final trilogy of the Star Wars Saga, The Hollywood Reporter said Friday.
The story will focus on the Skywalker family -- comprised of Darth Vader/Anakin Skywalker, and twins Luke and Princes Leia. The story would feature Mark Hamill (Luke) and Carrie Fisher (Leia) as older versions of the characters they made popular in the 1970s and 80s, the entertainment publication said.
Citing sources whose names it did not report, The Hollywood Reporter said a number of other characters from the first six films could appear in the final three.
Lucasfilm's Kathleen Kennedy has yet to name a director for the project, though "The Incredibles" director Brad Bird has been mentioned in connection with the series.
Arndt won an Academy Award for his screenplay for "Little Miss Sunshine." His next project is co-writing the "Hunger Games" sequel "Catching Fire."