Last month, Peaches was forced to deny claims that she had taken heroin after a man she allegedly slept with posted nude photographs of her online.
However, the Daily Star claims that Bob Geldof believes his daughter is at risk of having an overdose like her mother Paula Yates, who died in 2000.
"Bob was livid," a source said. "Especially after what happened to her mum. But Peaches was really tearful. She kept apologising and told him her drink and drugs days are over. She claims she's clean now and there's no need to go to rehab."
The insider also said that Peaches accepts why she was fired from underwear brand Miss Ultimo.
"She claims she's 'clean as a whistle' now and that she's got good friends in LA who'll keep her on the straight and narrow," the source continued. "We hope she's right, but she's still going out most nights and she's certainly not leading a quiet life."
Meanwhile, family friend Gerry Agar revealed that Bob Geldof is supporting Peaches, adding: "He knows he's fighting a losing battle but he's scared that pushing her too hard will mean he loses her for good. That's the last thing he wants to happen. He's going to have to grin and bear it while she learns from her mistakes."
Friends of Yates recently expressed concern about Peaches' behaviour.