Donald Trump's name-calling is apparently getting aggressive in private ... 'cause a new report claims he's calling his presidential opponent a brutal name behind close doors.

The New York Times published a piece today diving behind the scenes of the Trump campaign over the last few weeks ... and, in it, the Times details what they call the "foul mood" Trump's been in over the last few weeks.

Among other alleged angry actions and remarks ... NYT says two anonymous sources claim he's called Kamala Harris a "bitch" multiple times -- and, he's reportedly attacking her at donor events too.

NYT reporters provide details about his fundraising dinner in the Hamptons -- and, they say some of the attendees were also shocked about Trump doubling down on recent comments about Harris' race.

Remember ... while speaking to the National Association of Black Journalists, Trump claimed Harris only recently began identifying as Black -- comments that landed him in hot water last week.

NYT says he told attendees he still thinks he's right despite all the backlash he's receiving ... before apparently going on a rant about KH.

Now, Trump reportedly using a swear word to attack his opponent isn't unique ... remember, back in February reports came out that Joe Biden regularly refers to Trump as a "sick f***." Video evidence seems to show him nearly doing it at a rally.

Worth noting ... Trump spokesman Steven Cheung told us DJT has never called Harris a "bitch" -- adding the campaign wouldn't characterize her as such either.

We've reached out to Trump's camp for more clarification ... so far, no word back.