"Mary has not filmed anything this season and they just started this week," the source says.
Fans have speculated that Cosby, 49, would be exiting RHOSLC after she skipped the season 2 reunion, which was filmed earlier this month.
During a conversation on Twitter Spaces Tuesday, Cosby explained her decision, saying, "The only thing I have to say about the reunion is I didn't go because it was one-sided."
Chad Kirkland/Bravo Mary Cosby
The source says Cosby's absence came as a shock to her costars, though. "The cast had no idea that Mary wasn't attending the reunion," the source says. "She didn't tell any of the ladies she wasn't coming. They were all shocked she didn't show."
The news that Cosby is not filming season 3 comes after costar Nguyen faced backlash over old Facebook posts of hers that allegedly resurfaced.
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On Wednesday, Nguyen issued an apology on Instagram for the posts, some of which criticized the Black Lives Matter movement, the nationwide protests and riots following the death of George Floyd, and more, according to Page Six.
"I want to acknowledge and apologize for my deleted Facebook posts from 2020 that resurfaced today," Nguyen began her statement, which she captioned "#hateisavirus."
Chad Kirkland/Bravo Jennie Nguyen
"At the time, I thought I was speaking out against violence, but I have since learned how offensive and hurtful my words were," the reality star continued.
Shah, 46, later addressed Nguyen's past comments on her own Instagram page and slammed the apology as "disingenuous."
"Needless to say, we have some real s--- to talk about," Shah added.
Rose, 35, wrote on her social media that she was "shocked and saddened" to learn about the resurfaced posts, while Marks, 39, urged her followers to "use your voice to speak out against what is wrong and amplify those that are not being heard."
About the cast's reactions to Nguyen's previous posts, the source tells PEOPLE, "A lot of the ladies unfollowed Jennie. They have united together over their feelings on her comments and are all upset by them."