Pistorius’s lawyer Kenny Oldwage confirmed that they were in discussions with the Steenkamp family.
“You will understand this is a very sensitive situation,” he was quoted as saying.
Steenkamp and her half-brother Adam reportedly helped their pensioner parents Barry and June financially, including with the rent on their home.
Her parents have lodged a multimullion-rand civil claim against Pistorius for loss of income and emotional distress.
Pistorius’s lawyers want to settle the lawsuit before the outcome of the criminal trial.
Advocate Petrus “Dup” de Bruyn, for the Steenkamps, said ”nothing has been decided on yet”.
Steenkamp’s mother, June, declined to comment on the civil suit.
“This is just too much... we are grieving... missing our baby... our beautiful, beautiful daughter who should have been celebrating her birthday today [Monday],” June Steenkamp said.
Pistorius appeared briefly in the Pretoria Magistrate’s Court on Monday for shooting Steenkamp on February 14 in his Pretoria home.
His trial for alleged murder was set for March 3 2014.