The communication between the two families is over a possible out-of-court settlement that would compensate the Steenkamps for the killing of their daughter by the double-amputee Olympian, according to South African press reports.
A South African newspaper reported that negotiations were initiated by Pistorius' lawyers, who the paper said were "desperately trying" to negotiate a settlement before Pistorius goes on trial in March on a charge of premeditated murder for Steenkamp's shooting death.
Dup de Bruyn, the lawyer for the Steenkamp family, told The Associated Press that "the two sides are talking" but declined to comment further because of the delicate situation.
Before her death, Steenkamp reportedly gave financial help to her parents, Barry and June. She was killed by Pistorius on Feb. 14, with prosecutors indicting the world-famous athlete on a charge of premeditated murder Monday.
His trial is set for March 3-20, 2014 in the South African capital, Pretoria, where a conviction could also make him liable to a substantial civil suit by Steenkamp's family. Pistorius denies murder and says he shot Steenkamp by mistake, thinking she was a dangerous nighttime intruder in his house.
South Africa's Times newspaper reported that lawyers for Pistorius had approached Steenkamp's family, and the newspaper said Steenkamp's parents were seeking around $300,000 for loss of income and emotional stress.
"Pistorius' lawyers want to settle the lawsuit before the outcome of the criminal trial, in an attempt to reduce a possible payout," The Times said in its front-page story.
Pistorius is already under financial pressure because of his mounting legal bills.
The Times said Kenny Oldwadge, one of Pistorius' lawyers, "confirmed the discussions with Steenkamp's family."
"You will understand this is a very sensitive situation," Oldwadge said, according to the paper.
Oldwadge didn't immediately answer phone calls to his cellphone from the AP.
Steenkamp, a model and budding reality TV star in South Africa, would have turned 30 on Monday, the day Pistorius was indicted on charges of murder and illegal possession of ammunition.
Pistorius faces large lawyers' fees and is not earning any money after he took an indefinite break from competing to concentrate on his upcoming trial. His main sponsors also suspended their endorsements soon after Steenkamp's killing. The runner is reportedly trying to sell some of the houses he owns, including the villa where he shot Steenkamp, to raise money.
Follow Gerald Imray at www.twitter.com/GeraldImrayAP
Also on HuffPost