Pistorius was convicted of killing his girlfriend Reeva Steenkamp, whom he shot dead through a toilet door at his home in the early hours of Valentine's Day last year.
The athlete could face a maximum sentence of 15 years in prison, but his defence team believe that a correctional supervision term would be appropriate.
Ms Vergeer told the High Court: "It would break him as a person and take away his future, and place a broken person back into society. His rehabilitation has a far greater chance of success under custodial supervision than in prison."
Pistorius was cleared of murder after claiming that he mistook Steenkamp for an intruder when he fired the shots.