Fenty is following Rihanna in an attempt to make sure the "Umbrella" hitmaker, 24, is well looked after, reported Sun online.
"Monica is moving in to keep an eye on her. Rihanna's dad, Ronald, was a crack addict. Monica's refusing to let her go down that path," a source said.
Rihanna was recently rushed to hospital suffering from "exhaustion and dehydration".
However, after a brief stay in the undisclosed medical centre, she was discharged and allowed to fly back to her home in Los Angeles.