It is understood that US broadcaster, NBC, has offered Clinton the role for an entire season if he wants it. A decision is expected to be made by the end of this week.
First broadcast in 1975, 'Saturday Night Live''s previous guest hosts include Matt Damon, Robert De Niro, Salma Hayek and Christopher Walken, as well as former Vice-President Al Gore.
Fresh from addressing the Democratic National Convention in Boston last week, Clinton is back in the limelight, with a memoir to push as well as appearing on the 'Late Show with David Letterman' tomorrow to talk about the book, 'My Life'.
Clinton last appeared on the Letterman show in 2002 on the first anniversary of the September 11 terrorist attacks.
He was also on 'Richard & Judy' when he was in the UK, where he was interviewed about his personal life, including his affair with Monica Lewinsky, as part of his book tour.
'My Life' chronicles his time in office and a childhood that included growing up with the abusive stepfather he called "daddy". The book has received mixed reviews. In a positive piece in the New York Times recently, the paper said: "He can write -- as Reagan, Ford, Nixon and Lyndon B Johnson, to go farther back, could not." Since its release on June 22, the book has sold more than 1.5m copies.
Pirate copies have appeared in China where Clinton praises Chairman Mao and where he tells Hilary, on meeting her, she was a princess.
"She [Hilary] was as beautiful as a princess. I told her my name is Big Watermelon" and "China is a mysterious and unique place".
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