O'Neill, who returns to Villa Park for the first time since his untimely exit in August 2010 on Saturday, finished in sixth place in the Barclays Premier League table in each of his last three seasons with the Midlanders.
The Ulsterman returned to the game in December last year when he accepted the challenge of guiding the Black Cats away from the drop zone, and having achieved that and all but mathematically confirmed a sixth successive top-flight campaign, he is now setting his sights higher.
Asked if what he achieved at Villa can be replicated on Wearside, he said: "For Sunderland Football Club? Of course it's achievable, absolutely.
"It's achievable, the club is big enough to be able to have those sort of demands put on it, I am hoping.
"Whether we are able to do it or not is another thing, but that should be the ambition at the football club."
O'Neill finally ended months of speculation over his future when he left Villa just five days before the start of the 2010-11 campaign amid suggestions that he was unhappy with owner Randy Lerner's view on recruitment.
However, while the nature of his departure still clearly rankles, he was refusing to shed any light on the disquiet which prompted him to call it a day.
He said: "I had the privilege of managing one of the finest clubs in England, with a great tradition and great history, and I was there for four years.
"Things were a little sour in the final season - the irony of that was it was our best season.
"We finished in the top six and were about six points off the Champions League, and reached the semi-final of the FA Cup and final of the League Cup.
"But that can't be helped, sometimes these things happen.
"I am not going into any explanations today [Frday] of anything. I don't think on the eve of the match, that is the right time to do it.
"Maybe at some stage or another, the clearing-up of an issue or two might be useful, but it's not going to be today.
"That said, I am part of their past now and I hopefully belong to Sunderland's future, certainly the immediate future, and that's how I view it."
The game will see O'Neill renew hostilities with old foe Alex McLeish, a rivalry which was fostered during their time on either side of Glasgow's Old Firm divide.
Asked if their relationship was as frosty as that between Celtic and Rangers, O'Neill replied with a smile: "I never went out to dinner with him, put it that way - and I wouldn't want to have been seen in any corner of Glasgow eating with the Rangers manager.
"It might have been the last time I would have eaten myself."
O'Neill will send his ninth-placed team out looking to close the gap on Merseyside duo Liverpool and Everton immediately above them, but having seen them fail to score in each of their last three outings.
However, McLeish's problems are significantly more pressing with Villa sitting in 15th, just six points clear of the bottom three.
The Scot, of course, was not universally welcomed to the club after being handed the job despite presiding over city rivals Birmingham's relegation last season.
But O'Neill believes that whatever problems they are currently experiencing, there will be better days ahead.
He said: "I think Aston Villa will rise again to be a great club. It might not happen overnight, but it will happen."
Sunderland will have central defender John O'Shea back after a calf injury, but skipper Lee Cattermole, full-back Kieran Richardson and striker Connor Wickham will all be missing.