Burgess, who represented England in both rugby league and union and enjoyed a high-profile career in Australia's National Rugby League, was taken to Maroubra police station after failing the drug test, the reports said.
The former South Sydney Rabbitohs captain and now assistant coach was also given a court notice for allegedly driving with a suspended licence.
"After being pulled over... by an unmarked police car, an initial roadside drug test was taken, which showed positive to cocaine," Burgess said in a statement on Instagram. "A court date was issued for driving with a suspended licence.
"After I was released... I immediately and voluntarily went to an independent, internationally accredited testing facility and undertook a urine test. The urine sample returned a negative result to all illicit drugs.
"I deny any suggestion I have drugs in my system. I have not consumed, obtained, or possessed any illicit drugs. I have made positive improvements to my life and to my driving since my full licence was returned to me following a 10-month loss of licence."
Burgess has had issues with the law in Australia since retiring in 2019 due to a chronic shoulder injury.
In May last year, he was fined more than A$1,000 but spared conviction after pleading guilty to drug driving.
He was found guilty of intimidating his former wife's father by a magistrate's court in 2021, but the conviction was overturned following an appeal.
