'Today' show staffers reportedly want Billy Bush off the show permanently

Billy Bush may be getting the cold shoulder from his "Today" show co-workers.

Bush, who joined "Today" in August for the Rio Olympic Games, has come under fire after a tape from a 2005 interview with Donald Trump has been leaked and it shows Bush agreeing with Trump's objectification of women.

The "Today" show announced Sunday that they'd be suspending the 44-year-old anchor indefinitely as his behavior was unacceptable.

In an email to the "Today" show staff this weekend, show executive Noah Oppenheim confirmed that the the co-anchor had been suspended indefinitely from the show pending a review.

PHOTOS: Billy Bush and the 'Today' Show

"Let me be clear — there is simply no excuse for Billy's language and behavior on that tape," Oppenheim said in an email that was obtained by PEOPLE. "NBC has decided to suspend Billy, pending further review of this matter."

And while Oppenheim suggests that Bush could return, rumors are swirling that his co-hosts would be happy to show him the door.

An insider at the show told PEOPLE that Bush "hasn't really endeared himself to the rest of the cast and crew anyway, so they're fine with him leaving, if that's what the decision is."

"Ever since [Ryan] Lochte, a lot of people have thought that he was a liability anyway," PEOPLE's source explained. "Tamron [Hall] doesn't like him and they have always been uncomfortable around each other. Al [Roker] doesn't speak to him, like at all. There is no love lost there. Matt [Lauer] is okay with him, not friends, but okay. He doesn't have much of a relationship with Savannah [Guthrie]. So it won't be a loss to any of them personally if he doesn't come back."

"The network and producers are going to have to decide if he's such a liability that they have to take stronger action" adds the source. "Does anyone tune in to Today to watch Billy? Probably not really. So if he leaves, it's not a big deal."

Bush's co-anchors addressed his absence from Monday's show during the broadcast with host Savannah Guthrie explaining that Bush was under review.

There is reportedly a lot of gossip slinging off-camera as well, which likely won't bode well for Billy Bush.