Simpson was vilified last October after the wrong backing music track began playing during her live performance on the NBC late night staple, revealing she had been lip-syncing along to recorded music.
Simpson told Billboard she is in talks to appear as "SNL" host and musical guest Oct. 11 to promote her sophomore album.
"It's not confirmed yet, but I want to do it," she said. "I've battled those demons. I'm ready to go back out and do it again."