President Donald Trump had said the Goldman Sachs executive was on his shortlist of five people to replace outgoing ambassador Nikki Haley, who surprised many when she announced this week that she planned to depart at the end of the year.
But Powell spoke to the president on Thursday and asked that her name be removed from consideration, according to the person, who was not authorized to speak publicly about private conversations and spoke to the AP on condition of anonymity.
Powell indicated to Trump that she was honored to be discussed but felt it wasn't the right time for her family to take the post, the person said.
Powell, who has close ties to the president's daughter, Ivanka Trump, and his son-in-law, Jared Kushner, also told the president that she would be happy to continue to informally advise the White House.
Trump had told reporters earlier this week that he thought Powell would "love" the job, but said he was also talking to other potential candidates.
"We're certainly looking at Dina, and we're looking at others. There's some tremendously talented people," he said.
Others in the administration, including national security adviser John Bolton, had opposed the idea of tapping Powell for the position.
Colvin reported from Washington. Associated Press writer Zeke Miller contributed to this report.
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