The 28-year-old and fellow castmate Michaela Watkins will not return to the long-running NBC sketch comedy in the autumn after being axed by series creator Lorne Michaels this week.
Wilson told People: "I had an amazing time on SNL, and these rumours are completely untrue. And to clarify, the issue isn't that I'm too fat, it's that I'm too phat. Can I get a what-what?"
It was reported earlier that Jenny Slate and Nasim Pedrad have been added to the show as regulars.
Saturday Night Live begins its 35th season on September 26 with Megan Fox as host.