The Clydesdale Bank Premier League champions were placed in Group E, which also contains Spanish side Villarreal and Danish club Aalborg.

Celtic met United competitively for the first time in 2006-07, avenging a 3-2 defeat at Old Trafford with a 1-0 victory at Parkhead.

Japan midfielder Shunsuke Nakamura starred in both matches, scoring a stunning winner in the second game.

Villarreal will also be familiar opponents for Celtic fans, the Spaniards beating the Hoops 3-1 on aggregate in the quarter-finals of the UEFA Cup in 2004.

They also ended Rangers' dreams of reaching the Champions League quarter-finals in 2006 with an away-goals success in their last-16 clash.

Danish champions Aalborg, meanwhile, ultimately profited from Rangers' failure to reach this season's group phase.

They beat Lithuanian side FBK Kaunas, who shocked Walter Smith's men in the previous qualifying round.

Celtic are bidding to reach the knockout stage of the competition for the third straight season.

Striker Scott McDonald insisted they were confident of progressing, no matter the opposition.

"We went into the draw full of confidence anyway," he told Sky Sports News.

"Our home form's very good, it's just our away form that's been really poor in recent years in Europe.

"If we can try and get that right this year, that would go a long way to getting through to the next round."

McDonald believes it is a good omen that Celtic have drawn United and a Danish team in the same group.

"I think we always love to draw the champions of Europe as we did last year," he said.

"I think there's a few similarities from the last time we had Man United. I believe we also had a Danish team [Copenhagen] that time round.

"Hopefully, all these things add up to good things and get us through to the next round again."

As for the United games, he added: "They're going to be fantastic games, obviously.

"Two teams, Scotland and England, the rivalry already. In recent years, we played against them and we got a victory over them once and they beat us at their ground as well.

"It all bodes well for a great atmosphere and great game as well and hopefully we can give that to the public."

Chairman John Reid was amazed Celtic were in the same group as the holders for the second straight season.

"It's a big one, isn't it?" he said of being paired with United.

"We seem to make a habit of drawing the European champions!

"It's fabulous for Celtic fans. There are no easy groups, there are no free passes in Europe. We're just proud to be Scotland's representative in there and to be playing the European champions."

Describing Aalborg as "a bit of an unknown quantity", Reid added: "The three people we were talking to before the draw were Sir Alex Ferguson, the United people, Villarreal and Aalborg and we got the three of them there.

"We pipped United the last time at Celtic Park but there's no gainsaying the fact they're the European champions.

"They've got Cristiano Ronaldo, Alex Ferguson is a great manager. But Gordon Strachan's been doing very, very well.

"And if we've managed to beat people like AC Milan, Benfica, Man United and get through twice in a row to the last 16, wouldn't it be fabulous if we managed to to that again?"

Celtic chief executive Peter Lawwell was thrilled at the prospect of facing Manchester United again and sees no reason why the Scottish champions cannot progress to the knockout stages for a third successive campaign.

He told Scotland Today: "At this level, it's a formidable task to qualify but I think we've got a good chance. If we qualify three years running, it would be a remarkable achievement and I do genuinely believe we have a chance to do that.

"Overall, we are delighted. In Manchester United, we again welcome the European champions to Celtic Park. We know them well and we have a good relationship with the club.

"We remember the two epics we played two years ago at Old Trafford and the dramatic circumstances of the victory at Celtic Park. They were two great nights so we are really looking forward to it."

He added: "First and foremost, we are in this because it's the best football competition in the world and it's a privilege to be a part of that. The financials run alongside and are really important.

"But the privilege, the profile, the exposure that playing in this tournament gives you around the world is fantastic."

Lawwell refused to be drawn on whether Celtic manager Gordon Strachan will be allowed to strengthen his squad further before next week's transfer deadline.

"We are working on things," he said. "Time is obviously ticking again us but who knows?"