Billy Bush brazenly bragged to NBC staff about the vulgar Donald Trump tape while covering the Olympics in Rio, multiple sources tell Page Six.

Proving the infamous Ryan Lochte interview wasn’t Bush’s only Rio recklessness, the shamed “Today” host boasted at a party in August that he had a “tape of Trump being a real dog,” prompting staffers at “Access Hollywood” to track it down.

Bush never told NBC News brass about the tape when he joined “Today,” and they’re not happy about it. “Billy was bragging about the tape to other NBC staff while in Rio. If he knew about the tape, and remembered the full extent of such an explosive conversation with a presidential candidate and didn’t disclose that to NBC News, that is a very, very serious problem,” the insider said, adding it could violate the “morality clause” in his contract.

Another insider added, “It is not clear if Billy remembered the exact level of vulgarity in the conversation with Trump, or if he instead realized its news value and didn’t declare it to protect himself.”

Meanwhile, Bush could also be investigated by NBC for any signs of possible workplace sexual harassment because of the comments he made during his vile video chat with Trump about his ex-“Access” co-host Nancy O’Dell.

Bush appears to be egging on Trump as the bilious businessman talks about how he unsuccessfully tried to “f - - k” O’Dell. An NBC insider said, “There is concern that Bush didn’t defend his female co-worker. Instead, he appears to encourage that type of talk about her.” Bush is also heard commenting about an actress on NBC’s “Days of Our Lives,” Arianne Zucker, who he said was “hot as s - - t . . . All I can see is legs.”

An NBC insider said that female staff at “Today” revolted following the leak of the tape. A review of Bush’s actions is under way, and staff are being urged to come forward “with any concerns about Bush, his inappropriate behavior or frat-boy mentality.” Staff, particularly women, were polled about how they feel about Bush at a meeting at 30 Rock on Monday.

Meanwhile, Kathie Lee Gifford doesn’t even want Bush to “throw” the show to her and co-host Hoda Kotb. “She has Jesus in her life and feels this is just not right,” we’re told. Reps didn’t comment.

Warning: Explicit language