Fifty-seven percent of voters said they'd support a run by Clinton to succeed Barack Obama and 37 percent said they opposed, results of the poll released Wednesday indicated.
Clinton, a former first lady and U.S. senator from New York, was supported by 66 percent of women and 49 percent of men.
Clinton has said she would step aside as America's top diplomat after President Obama was elected to a second term. She also has said she has no interest in a second run for president. She waged an unsuccessful presidential primary bid in 2008.
Sixty-eight percent of Americans said they approved of Clinton's job as secretary of State, second only to Colin Powell -- who received an eye-popping 85 percent approval rating in 2002 and 2003 -- among the last five secretaries of State, ABC said.
Similarly, two-thirds of Americans in the latest ABC-Post poll said they viewed Clinton favorably, generally.
Results are based on a nationwide phone sample of 1,020 adults conducted Nov. 28-Dec. 2. The margin of error is 4 percentage points.