The six-time Paralympic champion was sentenced to five years in prison after being found guilty of culpable homicide.
The 27-year-old claimed that he mistook Steenkamp for an intruder when he fired four gunshots through a toilet door at his home in Pretoria, South Africa in the early hours of Valentine's Day last year.
June Steenkamp told The Times, who are serialising her book Reeva: A Mother's Story, that her daughter had "nagging doubts about their compatibility" and considered leaving him.
"She had confided to me that she hadn't slept with him," said June. "They'd shared a bed, but she was scared to take the relationship to that level.
"She wouldn't want to sleep with Oscar if she wasn't sure. I believe their relationship was coming to an end. In her heart of hearts, she didn't think it was making either of them happy."
June added: "Her clothes were packed. There is no doubt in our minds: she had decided to leave Oscar that night."
Reports have claimed that Pistorius will spend 10 months in jail before serving the rest of his sentence under house arrest.