Volpato was pulled over twice in one evening on the Anzac Bridge between Pyrmont and Glebe Island in Sydney, police say.
According to the police report, Volpato was pulled over by officers at around 11pm on Thursday night and fined for speeding 20km/h over the bridge's 60km/h speed limit.
At about 1am, police again intercepted Volpato after allegedly clocking his speed at 109km/h on the same strip of road.
A subsequent roadside drugs test had produced a positive result for cocaine.
Volpato had not admitted to taking drugs prior to driving that night, the report states.
He has not been charged with any offences, but a secondary saliva test was taken for further assessment.
An alcohol test conducted at the same time returned negative.
Having previously rejected Graham Arnold's advances as an 18-year-old in 2022, the New South Welshman made a last minute change of eligibility to represent Australia in May after pursuing a call-up to Italy's national team via his grandparental heritage.
After missing Australia's win over Turkey and appearing off the bench against the USA, Volpato started against both Paraguay and Egypt but was unable to register a goal contribution.
He finished with an average Flashscore rating of 6.6 out of 10 for the World Cup.
Volpato is currently on leave from Serie A club Sassuolo, who formally began their pre-season at the weekend with a 4-1 friendly win over Serie B club Padova.
Under Football Australia's drug policy, players and officials can be suspended for up to three months for testing positive to banned substances when used recreationally and not for performance enhancing purposes.
A three-month ban would see Volpato remain eligible for selection for the 2027 AFC Asian Cup, which begins in Saudi Arabia on January 7.
