As of Wednesday afternoon, the story was not available on the Web site.
The Los Angeles Times said NBC declined to comment on the development, but a show source not authorized to speak publicly about casting confirmed the news.
The Times did not say why she decided to leave.
Series regulars Kristen Wiig and Andy Samberg left the show earlier this year, and it is unclear how long Jason Sudeikis will stay.
The departure of Elliott -- who is known for her dead-on impressions of Rachel Maddow, Khloe Kardashian, Rosie Pope, Zooey Deschanel and Angelina Jolie -- is a surprise because she was expected to fill the void left by Wiig, the Times said.
Elliott is the daughter of comedian Chris Elliott, another former "SNL" player.