Pistorius, charged with the Valentine's Day murder of his Reeva Steenkamp, 29, was released on strict bail conditions two weeks ago. He was ordered to pay a bond of 1 million rand (£74,000), hand over his passports and forbidden from returning to his house, the scene of the crime.
Television channel eNCA said Pistorius and his lawyers felt his bail conditions were unfair.
"In papers before the high court they argue that Magistrate Desmond Nair was wrong to order Pistorius to hand over his passport and travel documents given that the magistrate found the athlete was not a proven flight risk," the report said.
Pistorius' defence said he should be allowed to travel if he won consent from the detective working on the case. They also argued that mandatory alcohol and drug tests were unnecessary and there was no need for him to report to a police station twice a week or be visited by a probation officer.
The case of the 26-year-old Olympic and Paralympic track star, a double amputee since infancy, stunned a nation that holds him up as hero who triumphed over adversity to compete with able-bodied athletes at the highest levels of sport.
On Thursday Warrant Officer Hilton Botha, the detective who was pulled off the investigation after it emerged he himself faced attempted murder charges, resigned from the force.
It is unclear when Pistorius' bail appeal will be heard.
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