Representatives for Pistorius in South Africa and the United Kingdom could not immediately be reached for comment by USA TODAY Sports.
Earlier, multiple media outlets in the country, including the Mail & Guardian and the South African Press Agency, citing local police, said the woman, 30, died at the scene at the athlete's house in Pretoria. The original source of the report appears to be Beeld, an Afrikaans-language daily newspaper. Local radio also reported on the fatal shooting.
Some media commentators speculated that the victim may have been in the act of surprising Pistorius for Valentine's Day.
Steenkamp had posted on Twitter about Valentine's Day on Twitter.
What do you have up your sleeve for your love tomorrow??? #getexcited #ValentinesDayPolice spokesperson Captain Sarah Mcirca confirmed to South African media that a woman was shot in the arm and head. A 9mm pistol was recovered at the scene.
Brigadier Denise Beukes told members of the media in South Africa that police were not the source of the report that the victim was mistaken as a burglar.
"We have also taken cognizance of the media reports during the morning of an alleged break in or that the young lady was mistaken to be a burglar," Beukes said. "Obviously our forensic investigation is still ongoing and we're not sure where this report came from. ... Our detectives have been on the scene, our forensic investigators have been on the scene and the investigation is ongoing."
South African police said that there had been "previous incidents" of a domestic nature reported at Pistorius' home.
Pistorius, 26, made history by being the first double amputee to take part in the Olympics.
Known as the "Blade Runner" for his use of carbon fiber prosthetic blades, Pistorius won gold medals in the 4 x 100 meter relay and 400 meter individual events at the 2012 Paralympic Games in London.
He was born without the fibula, the long, slender bone running along the outside of the leg from below the knee joint and down to the ankle, in each of his legs, information on his website says.
Pistorius is a huge star in South Africa and is viewed as an ambassador for the nation's sporting achievements. In 2012, Time magazine named him as one of the world's 100 most influential people.
He has sponsorship deals with brands including Nike, Oakley and the French fashion designer Thierry Mugler. He has appeared on the cover of numerous publications such as GQ and The New York Times Magazine.
The South African Sports Confederation and Olympic Committee said that it was not in a position to comment on the alleged fatal shooting. "Our thoughts are with the respective families at this time," the organization said, in a statement.
Speaking to CNN's Piers Morgan late last year, Pistorius said: "I grew up in a family where disability was never an issue. We didn't really speak about my disability, not because it was a topic that was taboo ... it was just never an issue. And that's the mentality that I've had."
The athlete's father, Henke Pistorius, told South Africa's SABC radio news on Thursday that he didn't know the facts. "If anyone makes a statement, it will have to be Oscar. He's sad at the moment."