Barry and June Steenkamp are seeking $300,000 from Pistorius for loss of income and emotional distress as a result of their daughter's death, The Times of Johannesburg, SA reported Tuesday.
Steenkamp and her half-brother Adam were helping their parents financially.
Steenkamp lawyers said "intense" negotiations with representatives of the Olympic athlete are proceeding.
Pistorius has been officially charged with the Valentine's Day shooting of Steenkamp. As a result, his lawyers are intent on settling the parents' civil suit before his homicide trial begins.
A family friend said the civil suit would be strengthened if Pistorius is found guilty of deliberating killing Steenkamp.
He has admitted shooting her through a bathroom door but said he thought she was a burglar.
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