Floyd Mayweather Jr. tried to re-connect with rapper T.I.'s wife on the red carpet of the BET Awards, but she was having none of it ... possibly to avoid another Floyd/T.I. brawl.

Tiny was doing an interview on the red carpet Sunday night when Floyd came rolling by with his girl. He tried to get her attention -- calling her name and trying to grab her elbow -- but she ignored him and just hightailed it out of there.

It's amazing that Floyd would do this, since ... as TMZ previously reported ... it was Floyd's relationship with Tiny that set off the Floyd/T.I. fight at Fatburger in Las Vegas last month.

Round 2, anyone?