T.I. never intended to get into a fight with Floyd Mayweather Sunday night in Las Vegas ... sources close to the rapper tell TMZ -- but Tip was definitely pissed about Money possibly getting close to his wife.

Tameka "Tiny" Cottle didn't appear to be near the fight last night -- but she was in Vegas -- and hours before posted a picture on Instagram while hanging out with Floyd's daughter ... calling the young girl her "new boo."

We're told T.I. was upset about the photo -- and others she posted -- and felt it was disrespectful to him ... so he planned to confront Floyd in person.

Once they got face-to-face though, T.I. flipped out when Floyd said "control your bitch" and started swinging outside Fatburger.

Shades of Sterling and Stiviano ... minus the racism.