The 31-year-old reality star discussed the 28-year-old sock designer and 36-year-old former NBA player on "Good Morning America."
Rob Kardashian was diagnosed with diabetes after a health scare in December, while Odom was transferred to a new facility this week after being hospitalized since October.
"Everything happens for a reason," she said of her brother's hospitalization. "If that's going to make him, like shake him up a bit and jump start his health journey, then great, I'm right here for him. He's taking it seriously. Yeah, we're only like 13 days into the new year, but that's good enough for me."
Kardashian said Odom is "doing really well" but has a "long journey" ahead of him in recovery.
The former Los Angeles Lakers forward suffered brain damage after being discovered unconscious in a legal Las Vegas brothel Oct. 13.
"Every day is different," the star said. "We take every day as it comes. I've learned not really look into the future ... I do believe that we're soulmates but that's not even where my head is at. I think people, they don't understand the severity of everything."
"There were a lot of challenges but he's a fighter and, obviously, he's here now and he's out of the hospital," she added. "It's all about his health and my happiness and his happiness and right now those are two individual things."
Kardashian filed to end her four-year marriage to Odom in 2013, but called off the divorce after his hospitalization.
The star, who is dating Houston Rockets shooting guard James Harden, later clarified her relationship with Odom isn't romantic, and candidly discussed the deterioration of their marriage Wednesday on "The Howard Stern Show."
"Lamar was so great at making feel like I was the only one and I'm this princess, I never speculated cheating," she said. "He was so good. Nothing was on his cell phone. He had an assistant and [the women were] all on his assistant's phone. He was really crafty. It's disgusting."
"All these rumors kept coming out in the weeklies," she recalled. "As much as I know that they're [expletive], I'm like, 'Where's there's smoke, there's fire' ... Then this one girl did an interview and she was so adamant."
Kardashian, whose flight to New York made an emergency landing in Las Vegas prior to her GMA appearance, expressed her hopes for Rob Kardashian in 2016 last week. She and her family continue to star on E! series "Keeping Up with the Kardashians," which airs Sundays at 9 p.m. ET.
DISCUSS AND COMMENT ON THIS STORY Reality TV World now offers Facebook Comments on our stories. To post a comment, log into Facebook and then 'Add' your comment. To report spam or abuse, click the 'X' in the upper right corner of the comment box.
Copyright 2016 United Press International, Inc. (UPI). Any reproduction, republication, redistribution and/or modification of any UPI content is expressly prohibited without UPI's prior written consent.