Speaking with Savannah Guthrie on NBC's "Today" show Tuesday, Kardashian, 32, said her younger sister, Khloe Kardashian Odom, "has been very open about her fertility issues and I think I was always really kind of quiet about mine, and I have similar issues, and so it was a pleasant surprise when so many doctors were telling me one thing and then the opposite happens."
She added: "That's an exciting moment -- you can't plan for things like that. So I think it's just such a blessing, knowing my circumstances."
Kardashian -- who appeared with the clan's eldest sister, Kourtney, to promote Sunday's season premiere of their E! reality show "Kourtney & Kim Take Miami" -- also addressed her extended path to divorce from Kris Humphries, from whom she separated on Oct. 31, 2011, 72 days after a wedding extravaganza shot for an E! special.
"I can't speak for anyone else," about why Brooklyn Nets forward Humphries, 27, hasn't proceeded to complete the divorce, she said. Humphries has claimed the marriage was fraudulent and done for publicity, a charge Kardashian denies.
Kardashian acknowledged that she and West, 35, might have the baby while she is still married to Humphries. "As much as I would love to be divorced, and we're working on it and I hope it's sooner than later . . . what are you going to do?"
Marriage with West is "something that we talk about," Kardashian said, "but it's just, right now, focusing on the baby."