"Rihanna doesn't bother me ...I want Chris [Brown] back" - Karruence Tran

Chris Brown's recently-dumped ex Karrueche Tran still believes she has a future with the singer -- in fact, Karrueche is telling friends, she's not gonna stop trying to get with Brown just because Rihanna's back in the picture. 

Karrueche was hurt when Brown gave her the axe a few weeks ago ... but she never stopped loving him -- and now, she is on a mission to get him back.

Karrueche reportedly got used to a certain level of celebrity while dating the singer, and she's not ready to "go back to being basic" -- even if that means messing around with Brown, while he's messing with Rihanna. 

Eventually, Karrueche hopes to edge Rihanna back out of the picture. "Rihanna doesn't bother me ...I want Chris [Brown] back" - Karruence Tran

Case in point -- Karrueche and Brown were spotted hanging out together Monday in Burbank ... two days after Rihanna and Brown were spotted together in L.A.

Chris Brown broke up with Karrueche earlier this month -- citing Rihanna as the reason -- saying, "I love Karrueche very much but I don't want to see her hurt over my friendship with Rihanna."