Waititi is already a Disney favourite following the success of Marvel film Thor: Ragnarok and Jojo Rabbit, which the studio acquired following the merger with Fox.
The latter picked up six Oscar nominations earlier this week, including one in the Best Picture category, and the former is getting a high-profile sequel titled Thor: Love and Thunder, which Waititi will also direct.
He also directed the season one finale of Disney+ series The Mandalorian, which is a Star Wars spin-off.
Originally, Lucasfilm planned for Game of Thrones creators David Benioff and DB Weiss to write a trilogy of Star Wars films, but they dropped out ahead of signing a lucrative deal with Netflix.
Rian Johnson, who directed The Last Jedi, was also set to return to the franchise, but is working on a sequel to his 20119 hit Knives Out instead.
Disney and Lucasfilm are yet to comment on the reports.