In court papers filed by Pistorius' lawyers on Aug. 11 and seen by Reuters on Thursday, his defence team says it will argue "a continuation of this matter is inimical to the interests of justice, patently unfair and that enough is enough."
The National Prosecuting Authority spokesman Luvuyo Mfaku said the case would be heard at the High Court in Pretoria next Friday before the original trial Judge Thokozile Masipa.
Pistorius is not expected to attend the hearing.
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The Paralympic gold medallist was sentenced in July for murdering his girlfriend, Reeva Steenkamp, in 2013.
The state said last month it would appeal the jail term, which was less than half the 15 years it had sought.
A Pistorius family spokeswoman could not be immediately reached for comment.
The track star was treated in hospital for wrist injuries earlier this month, but prison officials said Pistorius denied trying to kill himself. The incident coincided with the first day of competition in the Rio Olympic Games.
(Reporting by Tanisha Heiberg; Writing by James Macharia; Editing by Andrew Roche)
