The 29-year-old actress would like to follow in the footsteps of her fellow Hollywood stars including Emma Stone and Justin Timberlake and be invited to front the popular sketch show.
Asked whether the role was of interest to her, Olivia said: "That would be so much fun! I'm a big fan. It'd be great."
Referring to the star's fiance, Jason Sudeikis, who is a regular cast member on the show, E! News joked: "You have an in", to which Olivia quipped: "Do you know anyone?"
The actress famously met Jason on the 'Saturday Night Live' finale in 2011 just after her divorce from ex-husband Tao Ruspoli, and was initially worried the funnyman was out of her league.
Meanwhile, the 'Incredible Burt Wonderstone' actress also revealed she enjoyed seeing her male co-stars Steve Carell, Jim Carrey and Steve Buscemi spending as much time as her in the dressing room getting on the set of their new magician comedy.
She laughed: "Now they know what it's like! Wigs are not comfortable - and all the tanning and the shaving. It was hilarious. It was like being on [reality show] 'Toddlers & Tiaras!' "
Million dollar Ashford Castle wedding for Rory McIlroy and American bride Erica Stoll