Khloé Kardashian Shares Lamar Odom Health Update: 'I'm So Proud of the Strength That He Has'

01/06/2016 AT 07:45 PM EST

Khloé Kardashian is proud of how hard her estranged husband Lamar Odom is fighting for his health.

"Because it's not my story to tell, I try to respect that and I want him to be able to tell that story," she told reporters at a TCA panel promoting her upcoming FYI network talk show Kocktails with Khloé. "I'm just there to support and care for him."

She added that Odom, 36, is "doing amazing."

Khloé Kardashian Shares Lamar Odom Health Update: 'I'm So Proud of the Strength That He Has'| Health, TV News, Khloe Kardashian, Lamar Odom

Khloé Kardashian

Chris Weeks / Getty

"I'm so proud of the strength that he has to fight this battle that's his battle and I'm so grateful for everybody's love and concern, because I think it is coming from a good place," Kardashian, 31, said of Odom, who was found unconscious in a Las Vegas hospital in October.

RELATED VIDEO: Khloé Kardashian Wanted Lamar Odom Transferred to L.A. So He Can Get the 'Best Medical Treatment Possible,' Says Source

Kardashian also revealed that she was interested in watching FX's upcoming American Crime Story, which centers on the O.J. Simpson trial. Her late father Robert Kardashian (played by David in the series) was one of Simpson's defense attorneys, and Kardashian says her mother Kris Jenner has become friends with Selma Blair, who plays the Kardashian-Jenner matriarch.

"She was at our Christmas Eve party. My mom has way more investment into that movie," Kardashian said. "She helped out a little bit with some of the other characters, so I would like to see it, but it's neither here nor there. However they want to portray us is fine, but I'm still just interested."

Khloé Kardashian Shares Lamar Odom Health Update: 'I'm So Proud of the Strength That He Has'| Health, TV News, Khloe Kardashian, Lamar Odom

Kocktails with Khloé executive producer Craig Piligian and Khloé Kardashian

Jerod Harris / Getty

Kardashian's update on Odom's health comes as a source told PEOPLE that the former NBA pro will move from Cedars-Sinai Medical to a live-in rehabilitation center.

"The plan is for him to move in the next few days," the source said. "At the center, Lamar will continue to receive amazing therapy. He still has many challenges but is making progress. He is a fighter!"

Kocktails with Khloé premieres Jan 20 at 10 p.m. ET on FYI.
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