Oscar Pistorius during his Pretoria Magistrate's Court appearance on Monday 19. (Madelene Cronje, M&G)
The Times reported on Tuesday that 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's parents have lodged a multimullion-rand civil claim against Pistorius for loss of income and emotional distress. Steenkamp and her half-brother Adam reportedly helped their pensioner parents Barry and June financially, including with the rent on their home.
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 trial schedule
Meanwhile, prosecutors and the runner's defence team on Monday said they agreed to schedule his trial in the North Gauteng High Court between March 3 and March 20 next year – just 14 days for what is already clear will be a complex matter, with over 100 witnesses to testify.
A formal indictment on charges of murder and the illegal possession of ammunition was formally served on an occasionally emotional Pistorius as scheduled in the Pretoria Magistrate's Court during his 12-minute appearance on Monday. The indictment lists 107 witnesses for the state, including at least 18 of Pistorius's neighbours in the upmarket housing estate where he shot Reeva Steenkamp, a long list of police officers and forensic experts, paramedics, former girlfriends of Pistorius and several of his family members.
Also among the witnesses listed is footballer Mark Bachelor, who says an argument with Pistorius escalated to the point where the latter threatened to break his legs.
Though the witness list indicates that prosecutors intend to paint Pistorius as a man of high temper with a fondness for guns and a poor attitude towards women, the indictment also shows they will argue he intended to commit murder, even if he did believe (as he has willingly declared) that he thought he was shooting at an intruder.
"The accused said to witnesses on the scene that he thought she [Reeva Steenkamp] was an intruder," the indictment for murder reads.
"Even then, the accused shot with the direct intention to kill a person. An error in persona will not affect the intention to kill a human being." – Sapa; additional reporting by Phillip de Wet