The Hoops midfielder slammed in a dramatic late penalty in the Group G decider against Spartak Moscow at Parkhead on Wednesday to seal the 2-1 win and a place in the knockout stages of the competition along with Barcelona.
Neil Lennon's men could face United, Malaga, Juventus, Bayern Munich, Borussia Dortmund, Schalke or Paris St Germain when the draw is made on December 20.
Celtic beat Barcelona 2-1 at Parkhead on their way to reaching 10 points and it is that victory which Commons holds up as evidence of the Scottish champions' confidence.
However, Scotland international Commons, who played for Stoke, Derby and Nottingham Forest before his move to Celtic in 2011, would like another trip to Old Trafford.
"I think we can beat anyone on our day, we have proved that, not only in the SPL but in Europe, we can beat top, top sides," said Commons.
"With our fans and the way we set out to win games, I don't think anyone will fancy coming to play us. So it's going to be a tough draw for whoever it is.
"There are a few really tough sides but being a boy from down south, I would like to play Man United.
"I've played them before a couple of times but I was a Man United fan as a kid so for me, to get the chance to play against that club and play at that stadium again would be a dream come true again."
Good squad
Commons also believes they have proved their doubters wrong by reaching the last 16 of the Champions League.
"I remember doing an interview before the first game against Benfica and I was asked what the target was and I said that we wanted to qualify out of the group," added Commons.
"There were a few smiles and sniggers.
"We were quietly confident that we could give anyone a game on our day, we had a good squad who were trying to succeed and I feel we have proved a lot of people wrong.
"People who have not cost a great deal of money have come into the squad and turned out man of the match performances at home and away from home in Europe.
"We have turned boys into men and we have young players who are hungry for the game."
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