Clinton, who has spent two decades in the national spotlight and narrowly lost her own bid to be president in 2008, said she enjoyed her job as the top US diplomat but found it physically grueling.
Asked by talk-show host Tavis Smiley if she would serve eight years, she replied: "No, I really can't."
"The whole eight -- that would be very challenging," she said in the interview broadcast Wednesday on public television.
"It's a 24-7 job and I think at some point, I will be very happy to pass it on to someone else," Clinton said.
Clinton repeated that she would not run again for president, saying she wanted a private life after a career in which she has served as first lady and a US senator.
"There are so many things I'm interested in, really going back to private life and spending time reading and writing and maybe teaching. Maybe some personal travel -- not the kind of travel where you bring a couple of hundred people with you," she said.
Clinton said she also hoped throughout her life to be a strong advocate for the rights of women and girls.
The interview was broadcast the same evening that Obama delivered his first State of the Union address, which Clinton missed as she was in London to attend international talks on Afghanistan and Yemen.
By tradition, one member of the cabinet stays away from the president's annual address to Congress as a precaution in case of calamity.
As Clinton was overseas, that was not her. Housing and Urban Development Secretary Shaun Donovan stayed away in an undisclosed location.
Secretaries of state in recent times have rarely served more than one presidential term, although George Shultz was in office for six and a half years under Ronald Reagan.