Diddy's alleged terrorist threat involved a bomb ... an f-bomb ... with sources telling TMZ Sports the rap mogul threatened to "f**k up" the UCLA strength coach during their office fight.
Law enforcement sources tell us ... after Diddy swung a kettlebell at strength and conditioning coach Sal Alosi, he allegedly screamed out that he was "going to f**k him up."
Prosecutors believe the comments amounted to a "terrorist threat" -- so that's why he was hit with the charge in addition to 3 counts of assault with a deadly weapon.
As far as the case goes, one insider tells us important UCLA officials met this morning and we're told "charges will most likely be dropped but [Diddy] won't be allowed on the field anymore."
8:15 AM PT -- More info on what led up to the confrontation ... sources tell us the drama began earlier in the day on Monday when Sal booted Justin from a conditioning session for "lack of effort."
When Diddy -- who was a once-a-week regular at UCLA practices -- heard about the situation, he was PISSED and stormed down to Alosi's office with Justin.
When they arrived, Alosi was on the phone and told Diddy and Justin to hold on -- which only made them more upset. Alosi told Justin he would speak with him ... but instructed him to get his father OUT of the office.
This only pissed Diddy off even more, according to BruinReportOnline.
Alosi reportedly had his hands up in a non-threatening way ... but Diddy "walked into Alosi's hand" ... and then warned Alosi not to put his hands on him.
That's when Diddy exploded and attacked Alosi -- interns rushed in to break it up. Diddy was pulled out of the office and into the connecting gym, where he picked up the kettlebell and swung.
Alosi reportedly suffered cuts on his face and a torn shirt.