He is believed to be stepping down over concerns that he will be unable to deliver a quality film to 20th Century Fox's schedule, reports Deadline.
The rumour remains uncertain, with Fox declining to comment.
Andy Serkis is attached to reprise his motion capture role in Dawn of the Planet of the Apes, with original writers Rick Jaffa and Amanda Silver returning to work on the first draft screenplay by Scott Z Burns.
Wyatt is also currently attached to the Charlize Theron-starring Agent 13.
Dawn of the Planet of the Apes is scheduled for release on May 23, 2014.
Watch Rupert Wyatt talking to Digital Spy about a sequel to Rise of the Planet of the Apes below: