Last year they wrote to Rousseff asking for presidential pardon for their daughter.
"If we could have five minutes of her time, it would be an honour," Swanepoel told the newspaper.
Beetge was found with 10.2kg of cocaine in her luggage at Sao Paulo's Guarulhos International Aiport in 2008.
The Saturday Star reported that Marie and Gert Swanepoel have written to the Brazilian Embassy in Pretoria requesting a meeting.
Last year they wrote to Rousseff asking for presidential pardon for their daughter.
"If we could have five minutes of her time, it would be an honour," Swanepoel told the newspaper.
Beetge was found with 10.2kg of cocaine in her luggage at Sao Paulo's Guarulhos International Aiport in 2008.
Just R20 for the first month. Support independent journalism by subscribing to our digital news package.