NBC has declined to comment on Elliott's future, but a production source has told the New York Times that the actress won't return to SNL this fall.
Elliott was first rumoured to be departing Saturday Night Live in February when she was cast in the Fox pilot Ben Fox Is My Manny.
Her role on the pilot was later recast and Elliott returned to the NBC sketch comedy series to finish out the season.
Elliott - who joined SNL in 2008 - was best known for her impressions of New Girl star Zooey Deschanel and original character Fur Coat Rhonda.
The actress also has a long familial connection to Saturday Night Live. Her father Chris Elliott was a cast member from 1994 to 1995 and her grandfather Bob Elliott guest starred on the late-night series in the 1970s.
Abby Elliott previously described Saturday Night Live's breakneck pace as a "cocaine schedule, but without the cocaine".
Saturday Night Live is expected to kick off its new season in September on NBC.
Watch Abby Elliott in a Saturday Night Live sketch below: