"I don't want to talk about it," he initially tells his co-host, Kristian Murda Murphy, about the moment. Cheban then goes into it, saying that he was hanging out with former Dancing With the Stars pro, Maksim Chmerkovskiy, when they saw Odom, who was competing on the ABC show at the time.
"He said, 'You wanna say hi to this guy?'" Cheban says Chmerkovskiy asked him, referring to Odom. "And I said, 'I'm good.' Because Lamar and I don't have a friendship at all. There's zero [relationship there], so I'm like, 'Why would I randomly say hi to somebody?' We never, like, really spoke even when he was with Khloe. And also, I don't want to be a distraction to somebody."
Cheban further explains, "So, I'm like, 'No, I'm good.' And apparently Lamar heard it, and I was mortified."
Murphy notes that Odom allegedly replied, "I'm good too, bud."
Cheban is adamant that he didn't mean to offend with his comment, and he didn't expect to be overheard. "I just don't want to be a distraction. I don't know him like that. I was at the wedding, but I don't even think I said hello to him," he says of Kardashian's ex-husband.
"We never connected. He's not my boy. Tristan [Thompson]'s my boy. No, just kidding. I got a lot of s**t for that. Not going back to that," referencing his recent comments about Kardashian's other ex.
Cheban also tries to stir up a little drama when he talks about seeing Christie Brinkley on the set of the show following her injury. She was replaced on DWTS by her daughter, Sailor Cook Brinkley.
"Christie Brinkley got out of the car in front of us, she's stunning. There was no cast," he says, noting that Brinkley quit the competition over an injured arm. "I think Wendy Williams was right. I mean, Christie's beautiful like a flower, but it could have been fake. I don't know. How do you break your arm and not have a cast the next day at all?"
Odom, who was eliminated this week on DWTS, didn't mention the run-in with Cheban on Tuesday's ET Live, but he did talk about an almost run-in with Kardashian and her sister, Kylie Jenner.
"You know what's so funny, people were telling me about that. I didn't see them in the club that night," he told ET. "I didn't see them. I guess that's why they call it club Hyde."
He added, "No, I wasn't hiding but it's dark in there. It's dark in there and it's just probably hard to see people. I ran into LeBron James that night, but I didn't see Kylie or Khloe."
Here's more from ET's exclusive interview with Odom: