Gleb, 37, and his wife Elena Samodanova, 36, announced earlier this month they had decided to call it quits on their relationship after 14 years of marriage, with Elena accusing Gleb of "ongoing infidelity" and "a recent inappropriate relationship" that broke her trust.
The source told Us that Gleb and Chrishell's immediate connection led to the pair "texting a lot and hanging out outside of work."
"Chrishell and Gleb are still texting all the time and have been in contact about the public frenzy surrounding them," the insider told the magazine, referring to Gleb's separation from his wife.
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"Chrishell isn't bothered by the attention either. [She] isn't concerned about what [her estranged husband] Justin Hartley thinks of it all and is super over him and has moved on and is focused on the next thing."
As for whether there's a chance Gleb and Chrishell will date in the future once the dust settles, the source explained they're "just having fun and neither of them are expecting/wanting their relationship to become serious."
Chrishell's Selling Sunset co-star Amanza Smith believes Chrishell is pretty upset with the rumors circulating about her relationship with Gleb.
"Poor Chrishell," Amanza reportedly said during an interview on FUBAR Radio on Thursday.
"She was like, 'I went through a very public divorce. Like, the last thing she would ever do is add to somebody's infidelity if that's what was going on.' But that's just how it goes when you are in the spotlight, but I think she's pretty pissed off about it."
Amanza added, "It sounds like maybe the wife is using this as, like, a cheap PR stunt."
Shortly after Elena and Gleb announced their split about a week ago, Chrishell denied playing any role in the breakup amid speculation she and Gleb had a secret fling.
"I am so saddened about the news of Gleb and Elena's split. It is unfortunate that this has caused rumors to swirl about my personal life," Chrishell reportedly wrote on Instagram Stories at the time.
Alluding to her own divorce from Justin, Chrishell continued, "Having gone through a public split myself, I would not wish this on anyone. As you can imagine, the countless hours of training, and dance rehearsals has created a strong supportive friendship, but nothing more. I wish nothing but the best for both Gleb and Elena during this unfortunate time."
But Elena later told People, "After 14 years of marriage, and multiple affairs, I've decided enough is enough."
"Gleb and I have created a family and multiple businesses together. But apparently, it just wasn't enough to keep our marriage strong. Gleb's ongoing infidelity and a recent inappropriate relationship has created turmoil in our marriage and absolutely torn our family apart."
Elena elaborated, "No wife should ever stand by and watch while another woman gifts her husband expensive presents, lures him out to dinners and seduces him at every turn. Last night was the final straw, and I can no longer turn my head the other way."
But Gleb subsequently denied engaging in a relationship with another woman and cheating on his wife.
"While I will continue to respect the privacy of my family, I will not stand by and allow false accusations and Internet rumors go unaddressed," Gleb told People in a statement, before insisting his relationship with Chrishell has been strictly a friendship.
"My relationship with Chrishell was and remains strictly platonic," Gleb said.
"Our friendship during our season on DWTS was not the reason for our split. Elena and I have had longstanding issues in our marriage. This has been an ongoing situation between Elena and I paired with poor timing."
Gleb added, "It was my deepest hope to keep our private life just that: private. I am saddened and disappointed to see that Elena has chosen not to do the same."
Chrishell's representative also backed Gleb's claims by denying allegations she had any romantic involvement with the Russian pro dancer.
"Any insinuation or accusation that Chrishell is in any way involved in the dissolution of Gleb and Elena's marriage is 100 percent categorically false," Chrishell's representative told People in a statement.
"To be clear: Chrishell and Gleb are in no way, and have never been in any way, romantically involved."
Elena first broke the news of her split from Gleb on November 6 in her Instagram Stories.
"After 14 years of marriage with my deepest sadness our road is coming to an end," Elena wrote alongside a photo of Gleb and herself.
The blonde mother of two then posted a quote on her Instagram account that seemingly accused Gleb of being at fault for the demise of their marriage.
"I don't hate you, i'm just disappointed you turned into everything you said you'd never be," the quote read.
Not long after Elena went public with the breakup, Gleb posted his own message on Instagram and confirmed the breakup.
"It is with a heavy heart that I tell you my wife and I are parting ways after 14 years of marriage. We still intend to co-parent our wonderful children together who we love so dearly, and we will strive to continue to be the best parents that we can to them," Gleb wrote alongside a family photo with Elena and their children.
"We ask that you respect our family's need for privacy and healing during this time."
Gleb and Elena's failed marriage may come as a surprise to fans since they just celebrated their 14th wedding anniversary in July and everything seemed to be fine between the couple.
"Two souls but with a single thought, two hearts that beat as one. Happy 14th Anniversary my love," Gleb wrote on Instagram at the time.
And Elena had posted a video montage of her relationship with Gleb over the years in honor of their anniversary.
"14 years Together!" Elena captioned the video clip, along with three heart emojis. "Real Love stories never have endings @glebsavchenkoofficial now it's 4 of us #love #family #14anniversary."
Gleb and Elena's split announcement came only days after Gleb and Chrishell were ousted from theDancing with the Starsseason after performing a steamy Viennese waltz together.
Chrishell gushed about her relationship with Gleb in an October Instagram post in which she showed off a massive bouquet of pink roses, which prompted speculation they might have had an inappropriate relationship.
"OK full disclosure, @glebsavchenkoofficial and I had our first fight-ha! If apologies look like THIS, I guess it's not so bad!!" wrote Chrishell, who split from Justin in November 2019 and recently revealed onDancing with the Stars she's now single.
"We both care so much and I love the passion he brings to what he does. We are working on me picking up some of his strict Russian nature, and I am softening him up with a little southern charm. Finding the balance landed us here and I truly think this could be our best week yet #TeamSellingIt #DWTS."