Sesame Street posted the video Wednesday on YouTube and Facebook.
Introducing the tape, Cookie Monster says he wants to "branch out beyond me cookie-eating career."
The four-minute video follows with Cookie Monster doing a run-through of an episode of SNL.
He performs a brief opening monologue, a "MacGruber"-like sketch dubbed "Macarooner," a few "Weekend Update" jokes and a musical guest appearance as "Monster Gaga."
Cookie Monster likely wants to follow Betty White's lead. The 88-year-old White hosted an episode of SNL earlier this year after a Facebook campaign urged such casting.