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They reportedly want the matter settled before trial opens on March 3 next year.
The Steenkamp family lawyer Petrus de Bruyn confirmed discussions were underway, but refused to give details.
"We have both said that we are in talks with each other and that's all we are prepared to say," he told AFP.
The paper said Pistorius's lawyer Kenny Oldwage had also spoken of talks with the Steenkamp family.
But when contacted by AFP, Oldwage said: "I am not aware of these discussions and I can't comment."
Steenkamp and her half-brother had financially supported their parents, who are pensioners.
The support had included paying rent for their house in the southern coastal city of Port Elizabeth.
The parents are reportedly planning to lodge a civil suit claiming three million rand ($300,000) in damages.
The 26-year-old Pistorius wept and prayed in court on Monday before being served with his indictment for murder and given his trial date.
Steenkamp, a blonde cover girl and law graduate who would have turned 30 on Monday, died in the bathroom of Pistorius's upmarket Pretoria home in the early hours of February 14.
The double amputee athlete known as "Blade Runner", who is currently out on bail, has admitted to killing Steenkamp but denied murder, saying he shot her through a locked bathroom door because he believed she was an intruder.
Prosecutors will argue he is guilty of premeditated murder.
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The Steenkamp family lawyer Petrus de Bruyn confirmed discussions were underway, but refused to give details.
"We have both said that we are in talks with each other and that's all we are prepared to say," he told AFP.
The paper said Pistorius's lawyer Kenny Oldwage had also spoken of talks with the Steenkamp family.
But when contacted by AFP, Oldwage said: "I am not aware of these discussions and I can't comment."
Steenkamp and her half-brother had financially supported their parents, who are pensioners.
The support had included paying rent for their house in the southern coastal city of Port Elizabeth.
The parents are reportedly planning to lodge a civil suit claiming three million rand ($300,000) in damages.
The 26-year-old Pistorius wept and prayed in court on Monday before being served with his indictment for murder and given his trial date.
Steenkamp, a blonde cover girl and law graduate who would have turned 30 on Monday, died in the bathroom of Pistorius's upmarket Pretoria home in the early hours of February 14.
The double amputee athlete known as "Blade Runner", who is currently out on bail, has admitted to killing Steenkamp but denied murder, saying he shot her through a locked bathroom door because he believed she was an intruder.
Prosecutors will argue he is guilty of premeditated murder.
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