Mr Webber said the athlete has not returned to his upscale mansion since Ms Steenkamp was shot and "cannot contemplate ever returning to live there again".
Estate agent Ansie Louw, who is handling the sale of the Silver Woods Estate property, told The Independent the mansion will be sold in a closed bid.
No asking price has been set but the agency expects to sell the mansion for "no less than 5 million rand" (NZ$535,000). The family is determined to sell the house "as soon as possible" and hope to reach a deal on the price by mid-April.
Bidding kicked off earlier today and it has already attracted interest from several buyers, according to the agency. The house has been emptied and is in perfect condition for the new owner to move-in.
Pistorius was released on bail of one million rand (NZ$141,000) in February last year. The athlete has been paying his own legal fees since he was arrested on charges of murder.
The Paralympian's finances have taken a hit after losing lucrative sponsorship deals with Nike, reportedly worth $2 million, sunglasses maker Oakley, and French designer Thierry Mugler.
At the start of his murder trial, Pistorius pleaded not guilty of murdering Ms Steenkamp, claiming he shot her in a case of mistaken identity thinking she was an intruder.
Prosecutors argue he intentionally shot and killed his girlfriend following a domestic dispute. If convicted of murder he will almost certainly receive a life sentence, with a minimum term of 25 years in prison.
The case continues.