Rousey was out in NYC Monday night -- where she told us there's still hope for Floyd ... "He could go the Mike Tyson route and go on a journey of self betterment."
Mike had serious issues of his own during his storied boxing career -- his arrests include drug possession and rape. But people like Ronda truly believe he's a changed person now and he's completely rebuilt his image.
And according to Ronda ... Mayweather could do the same -- if he wants to.
There's more ... we also asked Ronda about her upcoming gig hosting ESPN's "SportsCenter" (she's pumped), and how she feels about Cher defending her UFC pal Nick Diaz, who was recently suspended for weed.
"I thought [Cher] was cool ... I didn't know she was THAT cool!"