Sources close to Eric the Jeweler -- who cranks out bling for 50 Cent, Snoop Dogg and many more hip-hop stars -- tell us Offset is the member of Migos who owes the $10k. Law enforcement sources confirm Eric said exactly that when he reported the fight and robbery of his $30k chain.

We're told Eric reached out to Offset multiple times about settling the debt, but was given the run-around. Then, when he bumped into Quavo early Monday morning at 1Oak, that's allegedly when the fight broke out. The jeweler suffered a swollen cheek, bloody nose and a bump on his head.

TMZ broke the story ... NYPD wants to talk to all the members of Migos and their manager. According to police docs ... Eric was jumped by Quavo and another man.

Still no word from reps for Migos.