Sir Alex Ferguson's men host the Spanish giants and their prolific forward Cristiano Ronaldo on Tuesday in the second leg of their Champions League last 16 tie, which is finely balanced after a 1-1 draw in Madrid last month.
While one of United's main tasks is going to be containing their former player, in 2003 it was a different Ronaldo who caused all the problems as the Brazilian scored a hat-trick to stop the English club progressing to the semi-finals.
"It wasn't one that I look back on fondly," midfielder Ryan Giggs, who will make his 1,000th professional appearance on Tuesday, told a news conference as he remembered a match that United won 4-3 although they went out 6-5 on aggregate.
"Every time you play in Europe you learn different lessons, certainly Madrid scoring early [in 2003] was always going to be an uphill task so hopefully that won't happen tomorrow night.
"If we do go a goal behind I think we've got the experience and the confidence to come back."
While hoping for a different result this time round, the 39-year-old Giggs reckoned fans could be in for another cracking game.
"When you get a game like that, so many goals, two great sides, it could be similar tomorrow," he said.
"When you get that much firepower on the pitch undoubtedly there's going to be chances and goals."
Ferguson, who will be without the injured Phil Jones who did a good job in man-marking Ronaldo in the first leg, warned his players not to get too hung up on the Portuguese.
"If we go in there worrying about the damage Cristiano can give us then we will forget about some of the things we can do ourselves," he said.
"Our main worry is not what happened 10 years ago but what is going to happen tomorrow."
He said the two Ronaldos were very different players.
"The older one - the fatter one - he was at a peak that time as a centre-forward," Ferguson said. "[Cristiano] Ronaldo is a supreme athlete... never misses a game, fantastic physique, pace, two feet, great in the air."
Ferguson agreed with Giggs that the game between two of Europe's biggest clubs was likely to produce goals.
"If we win 5-4 we're through, I think there will be goals tomorrow, I think both teams will score," he said.
"I think we are going to have to think we are going to have to score more than one."
Ferguson added United would need to put in a strong defensive performance to keep a lid on any breaks by the visitors.
"It probably will be the key to the game," he said. "I believe they are one of the best counter-attacking clubs in Europe... we've got to find a way of coping with that but also having our own threat in an attacking sense also."
One of those attacking threats could come from Giggs, who was looking forward to reaching his millennium milestone.
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