"There is a lot more to the story," Venardos told reporters. "It's not as if Quade and someone else has jumped in a car, packed their balaclavas and house-breaking implements and come down to the Gold Coast.
"But I am restricted in what I can say."
The centre, who has 11 international appearances and plays for Queensland Reds, said he hoped the case would not interrupt his career.
"I definitely hope I'm playing football -- that's what I love to do, so hopefully everything works out for the best," he said.
Cooper, who made his Test debut last year, was one of the successes of the Wallabies' grand slam tour of Britain and Ireland last month, where he played in all four internationals.
"Quade regrets putting himself in a position where he's left himself exposed to the allegations that he currently faces and he certainly regrets the potential embarrassment to his employers, the Australian Rugby Union and their corporate supporters, to his family and to his team mates," Venardos said.
"We'll continue to work with the ARU and the QRU (Queensland Rugby Union) to get to the truth of the matter and we'll be working with Queensland Police likewise to get to the truth of the matter," he added.
"I have, and Quade has, every confidence the truth will prevail and in the meantime we are just asking people not to prejudge the circumstances because it's a watch-this-space situation."