Lawyers for Pistorius, who goes on trial in March on murder charges for shooting dead Reeva Steenkamp, are mulling a settlement for loss of income and emotional stress, The Times reported.
They want the matter settled before trial opens on March 3 next year.
The paper said Pistorius's lawyer Kenny Oldwage had confirmed that they were in discussions with the Steenkamp family.
But 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 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.
Oscar Pistorius, the Paralympian gold medalist, was indicted today for murder and possession of ammunition after the fatal shooting of his girlfriend, his trial will begin in March.
South African Paralympian Oscar Pistorius will face trial in March next year charged with the murder of his girlfriend Reeva Steenkamp, a court ruled Monday.
"Mr. Pistorius, the matter is then transferred to the High Court and is scheduled to start on the 3rd of March 2014 and will run until the 20th of March 2014," magistrate Desmond Nair said.
Pistorius was handed a copy of the indictment and the court adjourned.
Paralympic athlete expected to face charges of killing his girlfriend, Reeva Steenkamp, seven months ago.
The 26-year-old sprint star walked into the Pretoria court on Monday wearing a black suit and light blue shirt, and started praying with his sister Aimee and brother Carl, holding hands with them and crying.
He will be indicted on the main charge of the premeditated murder of his girlfriend.
The indictment papers are expected to include a list of witnesses to be called by the prosecution and detail some of the evidence police investigators have gathered in the six months since Pistorius shot Steenkamp in a bathroom in his home on Valentine's Day.
The statement, from the office of South Africa's national police commissioner, said detectives, forensic experts, ballistics experts, psychologists and technology experts all worked on the case and are confident that they have the evidence to convict Pistorius.
The most telling evidence may be in records on mobile phones found at Pistorius' home and through examination of the toilet cubicle door, through which Pistorius shot four bullets, hitting Steenkamp three times and killing her.
The angle and trajectory of the bullets could show if Pistorius was standing on his stumps when he fired, as he says, or if on his prosthetic limbs, as the prosecution maintains.
Monday's hearing is expected to be brief and lawyers have already agreed to start the trial in 2014 amid backlogs in the South African courts. It should run for around a month.
"The trial will be in March next year. It will be from the first week of March until end of March," his attorney, Kenny Oldwage, told AFP.
A single senior judge will hear the case. South Africa does not have a jury system.
Pistorius, who is out on bail and faces a life sentence if found guilty, has denied murder, saying he shot Steenkamp through a locked bathroom door because he believed she was an intruder.
He broke down several times in court during his February bail hearing and family members have spoken openly about his trauma.
Voice of Russia, FOX News, Al Jazeera, AFP