The two injured backs were involved in a brawl with security guards at the Victory Hotel in the early hours of the morning after being evicted from the venue, Sydney's Daily Telegraph said.
The ARU has launched a probe into the incident, a spokesman said, while declining to provide details.
"We've been made aware of an incident overnight and are still making our own enquiries," he said.
"As a matter of process the issue will be referred to an ARU disciplinary review procedure. We have nothing further to add at this stage."
Staff and management contacted at the Victory Hotel declined to comment on the reports.
The incident comes as the Wallabies prepare for their series-opening Test against Wales in Brisbane on Saturday.
Neither Cooper nor Beale were named in the match-day 22 as they both continue their recovery from injuries.
Both have previously been the subject of disciplinary probes.
Cooper was fined by the ARU and ordered to undergo counselling after being charged with burglary in 2009 over the theft of laptops from a Gold Coast residence. Police later dropped the charges.
Beale, Cooper and James O'Connor were last year cleared by the ARU of any wrongdoing after a probe into reports they had fought among themselves in France on the Wallabies 2010 tour of Europe.