Hillary ClintonHillary Rodham ClintonApril Ryan: 'I was in shock' Is America's military effort in the Middle East constitutional? Spicer: Trump will 'help the team' if needed in Georgia special election MORE on Tuesday said the U.S. political system is not descending into a monarchy with the potential for another Clinton or Bush in the White House.
In an interview published in the German news outlet Der Spiegel, Clinton said there have been earlier presidents with the same last name, and speculated that some families have a predisposition for elected office.
Clinton and former Florida Gov. Jeb Bush are considered potential candidates for president in 2016.
She used her loss to Barack Obama in the 2008 Democratic primary to illustrate that she was not anointed.
"I ran for president, as you remember," she said. "I lost to somebody named Barack Obama, so I don't think there is any guarantee in American politics. My last name did not help me in the end. Our system is open to everyone. It is not a monarchy in which I wake up in the morning and abdicate in favor of my son."
On the subject of her daughter, Chelsea, Clinton said it is up to her whether she ever runs for office herself.
Clinton seemed wearier of another Bush in the White House but declined to comment on the potential candidacy of Jeb Bush.
"Well, there will be plenty of time to comment on that if indeed an election were to involve somebody with that last name, but I am not going to say anything about it now," she said.
Even Bush's mother, Barbara Bush, has expressed reservations about having another Bush or Clinton in the White House, previously saying there are more than a handful of capable families in the United States. Bush has since scaled back that rhetoric.
"I think the point she was making is understandable, but I also think in our democracy, anybody can run for any reason," Clinton said. "And his last name may factor into it. The color of his eyes might factor into it. His policies, I hope, factor into it."