Now 32, O'Driscoll could still face the Wallabies with the Lions in 2013 having previously done so back in 2001.
And when Ireland take on the newly-crowned Tri Nations champions this weekend, Ashley-Cooper admits he and his team-mates will have their work cut in stopping O'Driscoll in his tracks.
"Brian is a freak," said Ashley-Cooper, who started last week's win over Italy on the wing but has previously gone head-to-head with O'Driscoll in the centres.
"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'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.
"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."
Ashley Cooper may have established himself as one of the leading lights in world back play but O'Driscoll remains the old master according to the Brumbies star.
The Irishman has been the man to watch ever since Ashley-Cooper was starting out on the global scene and the 27-year-old Australian says he has learnt a lot from studying the former Lions captain's game.
"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," added Ashley-Cooper.
"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."