Kim and Reggie had already been having troubles for a few months . . . because their conflicting schedules were keeping them apart.

But Reggie hit the roof when he saw text messages from Kanye on Kim's phone, and that was pretty much the end.

A so-called "source" says, quote, "The texts referenced a night they hung out, how much fun he had, how hot Kim was, and more racy things that got Reggie's imagination running."

But Reggie might not be all that innocent himself. RadarOnline.com says that there's a, quote, "sexy Latina model in Miami" who claims she had an affair with Reggie for several MONTHS while he was with Kim.

They didn't identify her, but they said she's been threatening to sell her story to the highest bidder.