Ashley-Cooper has held the Ireland captain in the highest regard ever since being told as a teenager to study him in order to learn how an outside centre should play.
The 27-year-old utility back is an option to line-up opposite O'Driscoll in Saturday's World Cup showdown at Eden Park and he hopes he is given the nod.
"Brian is a freak. He created a pretty painful result for us at Croke Park a couple of years ago when he scored under the posts to draw the game," he said. "He's achieved so much. All of us in the Aussie camp respect him so much.
"On a good day he's one of the best in the world. We're hoping he has a quiet night on Saturday.
"Absolutely he represents the same threat that he did five years ago.
"Players like Brian turn up in arenas like this. It's a World Cup and he's here to play.
"Back in 2002 I was told by my coach to study Brian O'Driscoll because he was the best at what he did at 13.
"He had acceleration and defence - he's a complete player and has shown that for that last 12 years.
"I'm sure whoever gets the 13 jersey this week will be very excited to face him.
"If you want to be the best you've got to compete against the best and Brian has been on top of his game for so long."
Australia were crowned Tri Nations champions last month, but Ashley-Cooper insists that status has little relevance to the World Cup.
"We took a lot out of our last two performances, against South Africa in Durban and against the All Blacks in Brisbane," he said.
"To win such an important tournament has created a lot of confidence and belief in the squad.
"But we've put that behind us because these are new challenges. Ireland are going to be tough.
"It seems to me that games are being won around the 60-65 minute mark. We expect a pretty tight encounter right up until then."
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