Billy Bush's suspension from NBC's the Today show has caused quite the shake-up, but his fellowco-anchors are taking the news in stride.

"The staff is comfortable with how the situation is being handled," a source close to the situation tells ET of Bush's absence from the morning show.

WATCH: Today Addresses Billy Bush's Suspension Over His 2005 Conversation With Donald Trump

The 44-year-old TV personality's suspension comes after a 2005 recording was made public on Friday, where Donald Trump is heard making lewd comments about kissing and groping women to a laughing Bush, who was then a co-host on Access Hollywood.

As new reports allege that Bush's coworkers want him fired and that Today co-anchors Matt Lauer, Al Roker and Tamron Hall "strongly dislike" him, ET's source says, "Billy has a good relationship with each of the anchors and hosts. Let’s not forget Billy has been a part of the NBC family for a long time and they have all known him."

MORE: Donald Trump and Billy Bush Discuss Entertainment Tonight Host Nancy O’Dell in 2005 Recording

ET can also confirm that while some reports are saying that Bush doesn't fit into the Today show culture, he hasn't been there long enough for that to be determined. Bush didn't officially sign on to Today until after his coverage at the Summer Olympics in Rio de Janeiro, Brazil.

According to Brian Stelter, CNN's host of Reliable Sources and senior media correspondent, Bush had planned to appear on Monday's Today show. "He was planning to apologize on camera this time for his awful comment on that 2005 videotape," Stelter tells ET. "But on Sunday night, NBC bosses decided he would not get the opportunity to apologize at all. He would be suspended, and we don't even know for how long."

EXCLUSIVE: Nancy O'Dell Reacts to Donald Trump's 2005 Recording

As for Bush's future with the NBC morning show, Stelter adds, "It's very possible he'll never be back on the Today show."

Trump's comments to Bush in the 2005 recording were addressed during Sunday night's presidential debate. When asked if he'd ever committed sexual assault, as was alluded to in the tapes, the 70-year-old business mogul responded, "No, I didn't say that at all. I don't think you understood what was said. This was locker room talk. I'm not proud of it. I apologize to my family, I apologize to the American people."

A slew of celebrities spoke out on social media in regard to Trump's remarks at the debates. See their reactions:

^{Reporting by Amy Purnell.}

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