She told the Edinburgh International Book Festival that while she “abhorred” Donald Trump’s presidency, she has no current plans to follow in her parents’ footsteps.
She strongly criticised the US leader on issues such as the separation of children from their parents at the Mexican border, branding the policy “the greatest sin of the moment”.
“At federal level as much as I abhor so much of what President Trump is doing, I have a great amount of gratitude for what my congresswoman and my senators are doing to try to stop him at every point,” Ms Clinton said.
“While I disagree with the President, other offices that I could run for I think my family ... is being really well represented, but if that were to change, if my city councillor were to retire, if my congresswoman were to retire, my senators, and I thought that I could make a positive impact, then I think I would really have to ask my answer to that question.
“For me it’s a definite no now but it’s a definite maybe in the future because who knows what the future is going to bring?”
Ms Clinton, who was promoting her children’s book on women who have persisted against adversity, was also asked about how her mother Hillary Clinton had handled the loss of the 2016 presidential election.
“She just has continued to persist forward in trying to have a positive impact in politics and outside politics in the way that I have seen her do my entire life,” she said.
“Of course it’s not the way I wish she would be doing that because I think she would’ve been a uniquely extraordinary president, but I’m not remotely surprised that she hasn’t pulled the covers over her head because that’s just not who my mom is.”
She added: “I’m outraged every day by something our president has done or said or left undone or neglected, or who he has recently bullied on Twitter or television.
“For me, sometimes, I think I’m just so fundamentally my mother’s daughter that I’m far more outraged by the Trump administration ripping children away from their families at the border and not having reunified those children with their families now for months, than I am about anything he has ever done to my families.”
She continued: “In some ways I think this is the greatest sin of the moment in our country and we very much are doing everything we can to stop this from happening.”
Ms Clinton, who was just 12 when her father Bill Clinton entered the White House, spoke of how critics made fun of her looks and referred to her as a dog.
“I feel incredibly protective of Barron Trump, who is now 12 years old, the same age that I was,” she said.
“I disagree with his father on everything but people have made fun of, bullied him, for his appearance, or for him being more private.
“Equally I have no patience for that because he’s a child and he deserves a childhood as every child does.”