The US Republican presidential candidate has been invited to host the sketch comedy series by the show's executive producer Lorne Michaels, according to The New York Times.
"He was funny on Letterman, giving the Top Ten list," show writer Jim Downey said of Romney.
Romney has yet to answer the proposal. Should he elect to take the offer, he will likely be hosting next September.
Steven Spielberg made a cameo appearance on last night's (April 15) episode of SNL.
New York Giants quarterback Eli Manning will host the next episode of the series, with musical guest Rihanna, on May 5.