The former Democratic presidential nominee refused to rule it out, telling the BBC: "Never say never."
Mrs Clinton, 72, said she thinks "all the time" about what kind of president she would have been if she had beaten Mr Trump in 2016.
Seventeen Democrats are already vying to lead the party in 2020.
Speaking to BBC Radio 5 Live's Emma Barnett while in the UK on a book tour, Mrs Clinton was asked whether she would run again.
The former secretary of state, New York senator and US first lady replied: "I think all the time about what kind of president I would have been and what I would have done differently and what I think it would have meant to our country and the world.
"So of course I think about it, I think about it all the time. Being able to do that, and look, whoever wins next time is going to have a big task trying to fix everything that's been broken."
Pressed on whether she would throw her hat into the ring at the last minute, Mrs Clinton said: "I, as I say, never, never, never say never.
"I will certainly tell you, I'm under enormous pressure from many, many, many people to think about it.
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