US officials including President Donald Trump have declined to discuss Kim's condition after a report, downplayed by South Korea, that the reclusive authoritarian was ailing.
But asked in an interview, Pompeo said he had met Kim's powerful sister, Kim Yo Jong, whose recent elevation in the hierarchy raised pundits' view that she could be a successor.
I did have a chance to meet her a couple of times, but the challenge remains the same -- the goal remains unchanged -- whoever is leading North Korea," Pompeo told Fox News.
He renewed the US promise to bring the North Korean people "a brighter future" if the leadership gives up nuclear weapons.
"They've got to denuclearise. We've got to do so in a way that we can verify. That's true no matter who is leading North Korea," he said.
Pompeo flew to North Korea four times in 2018 as he arranged historic summits between Trump and Kim after more than a half century of enmity between the two countries.
But hopes for a breakthrough before US elections in November have dimmed, with North Korea firing off rockets and the United States refusing Pyongyang's demands for sanctions relief before full denuclearisation.
Daily NK, an online media outlet run mostly by North Korean defectors, said Kim had undergone a cardiovascular procedure earlier this month triggered by heavy smoking, obesity and fatigue.
CNN also quoted a US official as saying Kim was in "grave danger" after surgery.
But South Korea, which is technically still at war with the North, said it had detected no unusual movements in its neighbour.
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