The rapper is in London, while Osbourne is stuck in a hotel room, isolating herself after two of her granddaughters contracted COVID-19. Both are well, and she and her son, Jack, both tested negative. Her quarantine is up on Friday.
"It was a bummer. It was really a bummer not to be there," Osbourne told ET's Kevin Frazier about being quarantined, before touching on Osmond's surprise exit.
"We've had changes. People coming in and going. So we just go with the flow," Osbourne said. "I have to say that with four [hosts], we've got more time to talk."
Osmond was announced as co-host of The Talk in May 2019, joining hosts Eve, Inaba, Osbourne and Underwood following Sara Gilbert's departure a month prior. In early September, the singer revealed that she was exiting the show, explaining in a statement that she's currently working on other projects and is looking forward to spending more time with family.
“One of the highlights of my year at The Talk was working with my dear friend John Redmann, and I’m excited to continue our working relationship on several projects we are developing," Osmond stated. "Also, my husband and I just dropped our last two kids off at college, we looked at each other, laughed and remembered we hadn’t been this alone together since 1982!! So, at this stage of my life, I’m looking forward to spending more time with him and visiting all the kids/grandkids."
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As far as who Osbourne would like to see as a future co-host, she looks to her daughter and son. "If it was up to me, I'd have Kelly and Jack and, you know, laugh."
Osbourne, meanwhile, is adjusting to life in quarantine. The British TV personality has her two pups, Elvis and Bella, by her side and finds ways to keep busy. "I watch everything on the internet, everything on TV, and that's it," she shared. "I take the dogs out for walks. But I do it at night so there's nobody out."
She is, however, missing husband Ozzy Osbourne. "I miss him so much. He's like saying to me, 'When is this gonna end. It's like, Jesus, how long is this thing gonna go on for?' It just seems no end in sight," she said.
And while it's great that she gets to virtually continue her co-host duties, she admitted that "it's really, really hard" to be detached from the rest. "Zoom and everything is great, but not to be there, you don't really get the feeling of it," she said of filming at her hotel. "You just feel detached, which I am, and it's a bit of a bummer for me but next week!"
With her quarantine up in a couple days, she can't wait to reunite with her co-hosts and see the new stage.
"I love it," she said of the set. "I think that everybody's done a great job with it. It's separate enough that we're all safe, but yet we're all still touchable."
For more on Osmond's The Talk departure, watch below.