Stone, 17, caused a flurry of controversy when she moved in with 25-year-old music producer Beau Dozier, son of legendary Motown hit-maker Lamont Dozier, in Los Angeles suburb Encino. Stone is under California's age of sexual consent, which means Dozier could face statutory rape prosecution.
The Gap is famous for its clean-cut reputation, and the Daily Mail said Stone's possibly illegal living arrangement could make the clothing outlet see her as a liability.
However, Dozier denies the living situation is illegal.
"She's a British citizen and the legal age there is 16," he said.
A spokesman for Stone's family said: "She's not living or staying with her boyfriend -- she's in the care of his family."