Khloé Kardashian Opens Up About Lamar Odom's Emotional Trip to NYC and Rumors of a Romantic Reconciliation

02/23/2016 AT 06:00 PM EST

Khloé Kardashian says Lamar Odom stepping out in public for the first time since his health crisis was emotional for the Kardashian-Jenner family.

"He walks to Madison Square Garden, where he used to play," Kardashian said on Tuesday's The Talk of Odom attending her brother-in-law Kanye West's fashion show earlier this month. "Kylie [Jenner] is next to me, who has seen him walk. But she's crying ... it was so impactful. It was beautiful."

The moment followed months of ups and downs after Odom was found unconscious after a near-fatal overdose in a Nevada brothel. During that time, Kardashian, 31, called off her and Odom's divorce and ended her relationship with NBA star James Harden.

Despite speculation to the contrary, Kardashian reiterated that she and Odom are not romantically involved.

VIDEO: Inside Khloé Kardashian's Heartbreak after Lamar Odom's Hospitalization, 'This Is Exactly What She Feared'

"We're not back together. We're not at all," Kardashian said. "I love him with every fiber of my being. I think that's apparent. But we were married and I shared that union with him and I didn't want our divorce to happen, but it happened for many reasons. That doesn't mean I forget about this person in their time of need. I still believe in my vows of being there for him."

In a preview for Wednesday's Kocktails with Khloé, Kardashian opened up about the possibility of a reconciliation with Odom, noting it would "be like the best dream" but expressing doubt it would happen.

"Just building a friendship back is what I'm doing now," Kardashian said.

The Talk airs Weekdays (2 p.m. ET) on CBS.
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