Her body was discovered at the Paralympic and Olympic star's home in the Silver Woods country estate in the early hours of Thursday morning.
The circumstances surrounding the incident remain unclear but Beeld newspaper reported on its website that Pistorius accidentally shot Steenkamp after mistaking her for a robber.
Steenkamp had tweeted her excitement about Valentine's Day just hours before the shooting, which police say is being treated as a murder investigation.
Police spokesperson Brigadier Denise Beukes said that Pistorius was at his home after the death of Steenkamp and "there is no other suspect involved."
Beukes confirmed the pair were the only ones present in the house at the time of the shooting and said a 26-year-old suspect was undergoing blood alcohol and forensic tests and had made a request to be brought to court immediately.
Beukes said there had been "previous incidents" at Pistorius' home and that the suspect would apply for bail, but the South African Police Service would oppose the application.
Pistorius is expected to appear in court on Friday morning on a murder charge.
Pistorius is one of South Africa's national icons and was born without a fibula in both legs.
For years he has dominated in his category at Paralympic Games.
He races wearing carbon fibre prosthetic "blades" and reached the 400m semi-finals in the London 2012 Olympics.
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