The Hoops midfielder slammed in a dramatic late penalty in the Group G decider against Spartak Moscow at Parkhead to seal the 2-1 win and a place in the knockout stages.
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.
"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," Commons said.
"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."
Reflecting back on the campaign, Commons Celtic proved "all the doubters wrong" with their achievement.
He said: "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.
"There were a few smiles and sniggers. We were quietly confident that we could give anyone a game on our day."