Wojdan Ali Seraj Abdulrahim Shaherkani is due to compete in the +78kg judo category on Friday. A Saudi official said earlier this month that its female athletes would have to obey Islamic dress codes.
But last week, International Judo Federation (IJF) president Marius Vizer said Shaherkani would have to fight without a headscarf to comply with "the principle and spirit of judo".
Sunday's edition of Saudi Arabia's al-Watan newspaper quoted the father, Ali Shaherkani, as saying over the telephone from Britain that his daughter "will not compete in the Judo Games on August 3 if the committee insists that she removes her hijab".
Olympic and Saudi officials are in talks with judo chiefs in order to find a solution, IJF spokesman Nicolas Messner told Reuters on Friday. "We are confident a solution will be found," he said.
The father was quoted as telling al-Watan that he had not heard back from the International Olympic Committee (IOC) on the matter.
Female participation in sports has long been a controversial issue in Saudi Arabia, where conservative Muslim clerics have said it is immodest and goes against women's nature.
Until this year, Saudi Arabia was one of three countries, alongside Brunei and Qatar, never to have sent female athletes to the Olympics. Human rights groups urged the IOC to ban the countries from the Games unless they agreed to send women.
Saudi Arabia reached an agreement on the participation of Shaherkhani and Sarah Attar, an 800 meter runner, just two weeks ago after talks with the IOC.
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