Bush, 44, who was suspended indefinitely Sunday after he was heard in a leaked 2005 video engaging in lewd, sexist conversation with Trump, was in negotiations to exit
An NBC News representative declined to comment. Carson Daly has been filling in for Bush on the third hour of "Today" and is scheduled to be there Wednesday.
In the provocative tape, made while Bush was cohost of NBC's syndicated news magazine "Access Hollywood," Trump obscenely boasts about his ability to grope women with impunity because he is a celebrity. Bush is heard chuckling and encouraging Trump even as the reality show star crudely talked about how he tried to have sex with Nancy O'Dell, then a co-host on "Access."
Bush issued an apology for his behavior, saying he was "younger, less mature and acted foolishly in playing along."
But some female producers and personalities who work on the show — including Hoda Kotb and Kathie Lee Gifford — have made it known to NBC News management that they do not want to work with Bush, according to one person close to the program who was unauthorized to discuss the matter publicly.
Noah Oppenheim, the executive in charge of "Today," addressed the staff's outrage in an internal memo announcing Bush's suspension from the program Sunday. "I know we've all been deeply troubled by the revelations of the past 48 hours," he said. "Let me be clear — there is simply no excuse for Billy's language and behavior on that tape."
There was also an outcry on social media from female "Today" fans, many of whom threatened to boycott the show if Bush returned.
During the suspension, the company was said to be looking into Bush's past behavior as an NBC employee. He joined "Access Hollywood," which is part of NBC's syndication arm, in 2001. But it was unclear whether any other incidents were a factor in the network's decision to sever ties. It appears likely that NBC will have to buy out his contract, according to one TV agent who spoke on the condition of anonymity.
The decision to remove Bush happened swiftly, demonstrating an effort by NBC News to get past the controversy that broke when the tape was revealed Friday by the Washington Post.
The tape has been a major source of embarrassment for the network and became a major issue in Trump’s already turbulent campaign. The 11-year-old conversation was a prominent topic during the second presidential debate Sunday between Trump and Democratic presidential nominee
Bush joined NBC News in August as cohost of the 9 a.m. hour of "Today" with Al Roker and Tamron Hall; that he is fairly new to the tight-knit staff did not work in his favor.
The relationship between viewers and morning show hosts is among the most intimate in television. Although some members of NBC News management were willing to forgive Bush, there was concern he would be rejected by some audience members appalled by his behavior with Trump.
Angry viewers can result in declining ratings and revenue for "Today," an unacceptable scenario for the most profitable franchise on NBC. Advertisers raised concerns about Bush returning to the program after the tape had been seen by millions of people on newscasts and the Web.
Bush's offense risked alienating the female viewers who make up 68% of the audience watching the 9 a.m. hour of the "Today" show, which is more conversational and entertainment-oriented than the two-hour flagship that precedes it.
The 9 a.m. hour is also an incubator for the higher-profile anchor chairs.
Bush's arrival led to speculation that he was being groomed to eventually succeed Matt Lauer, who has been in the 7-to-9 a.m. co-anchor chair since 1997. NBC News executives probably do not want Bush to occupy the 9 a.m. seat if he has no future on the program.
Bush got off to a rough start on "Today" during NBC's coverage of the Olympic Games in Rio. He had the first interview with Ryan Lochte after the gold medal-winning swimmer and three of his teammates falsely claimed they were robbed at gunpoint. Lochte perpetuated his story during the interview with Bush.
After it was determined that Lochte was lying, Bush tried to excuse the swimmer's actions, which prompted Roker to chastise him on the air. The exchange went viral.
Bush is the nephew of former President George H.W. Bush and the cousin of former President
7:02 p.m.: This article was updated with additional information, including complaints from some female producers.
12:40 p.m., Oct. 11: This article was updated with new details about Billy Bush's exit from the "Today" show.