The comedy will focus on an uptight single mother (Elliott) and her laid-back brother who move in together to raise a child (Maggie Jones).
If Ben Fox is picked up to series, Elliott will be forced to leave SNL, according to Deadline.
The 24-year-old actress and comedian joined the NBC sketch show in 2008 and is known for impersonating the likes of Angelina Jolie, Khloe Kardashian and Zooey Deschanel.
She also appeared opposite Natalie Portman and Ashton Kutcher in the 2011 film comedy No Strings Attached.
Ben Fox Is My Manny has been scripted by Couples Retreat writer Dana Fox.
Other comedy pilots in the works at Fox include Living Loaded starring Donald Sutherland, Scrubs creator Bill Lawrence's Like Father with Eureka's Colin Ferguson, and the basketball comedy Rebounding.
> Abby Elliott: 'SNL has cocaine schedule without the cocaine'
Watch Abby Elliot discuss Saturday Night Live below: