O'Sullivan enjoyed a successful reign at the helm of Irish rugby as assistant and then head coach that ended in 2008, though major silverware always eluded him.
Ireland collide with the USA in their opening encounter in Pool C of the World Cup on Sunday and O'Driscoll knows O'Sullivan will be eager to shock his former employers.
"I've no doubt whatsoever Eddie will be fired up for this one. He'll be champing at the bit for this game," he said.
"I read a few comments that the USA won't lack motivation because it's the 10th anniversary of September 11.
"There's lots at stake in the match for USA, but Eddie has said his job will be to keep the players calm and controlled. He's got the experience to do that.
"I'm sure he'd love to get one over us, I don't know many coaches who don't want to get one over their old team."
O'Sullivan handed O'Driscoll the Ireland captaincy upon the retirement of Keith Wood in 2003.
"I enjoyed working with Eddie. It was a long period in my international career," said the Lions and Leinster centre.
"He had a huge part to play in my career. He did some great things for Irish rugby and was unfortunate not to win a Grand Slam.
"But he shaped the team to go on and achieve that. He deserves credit for that.
"When it comes to how much he knows about us, you can overread things. Players evolve and won't necessarily be the same as in 2008.
"Aspects of our game have changed. Plenty of new personnel have come in since he left."
One of the new faces is Conor Murray, the 22-year-old Munster scrum-half who will make his full Test debut against the USA on Sunday.
Murray continues his meteoric rise after only establishing himself in Munster's starting XV at the start of the year.
The squad's youngest member has yet to play in the Heineken Cup but did enough during substitute appearances against France and England last month to convince coach Declan Kidney he is worthy of selection.
"Conor is a confident young man. We were talking about him behind his back, about his probable man of the match performance in the Magners League final," he said.
"Although David Wallace picked the award up, the boys thought Conor was outstanding. He's shown great form and presence in training.
"I have no doubt he's up to the challenge. He's definitely got the right temperament for this.
"I've got to know him a little bit better as a person over the last few weeks. He's coming out of his shell a little bit.
"He's confident but not arrogant. He has good inner belief. His career is starting on a pretty good footing.
"It's not easy for a young guy like him to come into a squad. I was that person once upon a time.
"It's difficult to be yourself, you tend to stay in your shell a bit more and let others do the talking.
"But the more confident you get with your surroundings, your personality shines through.
"He's a lot more confident in the company of the Munster guys but we've seen signs that he's coming out of his sell.
"I've had some good laughs with him over the last week and he's a nice young fella."
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