The last time they did, the result saw them head back to Manchester with their tails between their legs, soundly beaten 3-1.
Even a victory at Old Trafford in the second leg could not take them through to the semi-final.
We have taken a look at United's team who lined up that night, and what happened to them.
Barthez would leave United a year later, being loaned out to Marseille and later sold to them. He then played for a season with Nantes before retiring in 2007. Only 41, he recently caused controversy by interfering in the Spurs goalkeeping 'row' over Lloris and Friedel which was stirred up by French manager Didier Deschamps.
It's impossible to miss Gary Neville these days; while he has retired from football, he is Sky's top pundit, a co-commentator, and even an England assistant to Roy Hodgson. He has been adding to the hype for tonight's match, describing Cristiano Ronaldo's ability as 'monstrous'.
Rio Ferdinand remains a United player and looks set to play again at the Bernabeu tonight after being rested at the weekend, and will be determined to ensure a better result than the mauling they suffered in 2003. How he performs here could determine his immediate future, with his contract up at the end of the season.
Brown went onto win the Champions League with United in 2008, but has since been moved on. He was sold to Sunderland a year ago, and is yet to recapture the form which saw Sir Alex Ferguson describe him as 'one of the best natural defenders of his generation'.
After leaving for a spell with Arsenal and then in the Bundesliga, Mikael Silvestre was actually back at Old Trafford earlier this year, training with the team in an effort to get fit and win a new contract. He didn't find a club in the Premier League, but has just signed a short-term deal in the MLS with the Seattle Sounders,
It isn't beyond the realms of possibility that Manchester United and David Beckham will face off in the Champions League Final. Beckham has just signed a deal with PSG until the end of the season who beat Valencia last night. Months after losing to Madrid, Beckham was signed by them for £25 million, where he spent three seasons, winning La Liga at his final attempt before becoming a two-time MLS champion with the LA Galaxy.
Keane was the captain of the side, lasting with the Red Devils before being 'booted out' by Ferguson in 2005. The midfielder went to Celtic, before going into management with Sunderland. He had a great start, but fell out with numerous players and left the post, before repeating the same with Ipswich. He can now be seen as an uncompromising ITV pundit and may be wheeled out in a fortnight's time when United are on the channel.
Butt keeps the lowest profile of any of United's fledglings. He left United in 2004, signing with Newcastle, where he spent six season. This included a short loan to Brimingham City, before ending his playing career in South China.
Giggs was playing and scoring for United just days ago, bagging the opener in the 2-0 win over Everton. The Welshman has had a glittering career and broke Sir Bobby Charlton's appearance record, and few would bet against him carrying on another season. He could be involved tonight, if off the bench.
The Ginger maestro remains a United player, but it's more than likely this really will be his final season. He retired once, and came back, but has been left out of the travelling squad tonight due to a recurring knee injury.
Ruud van Nistelrooy
Van Nistelrooy scored United's only goal of the game, and it wouldn't be the only goal he scored at the Bernabeu. He signed for Madrid in 2006, scoring over 60 goals for them, leaving for Hamburg in 2010. He returned to La Liga to spend a season with Malaga but retired in the summer.
Ricardo left for La Liga where he spent several seasons with Osasuna. The goalkeeper retired in the summer but came out of it in January to rejoin Osasuna to answer a SOS call due to injuries.
Laurent Blanc didn't have the greatest time at Old Trafford, and perhaps United could have done with the man he replaced, Jaap Stam in this fixture. Blanc is currently out of work after managing France's international team for two years, but says he wants to manage at Old Trafford one day.
Ole Gunnar Solskajer
Solskjaer would suffer terrible luck with injuries after the 2002-03 season, but he contributed to United's 2006-07 title triumph with 11 goals. He is currently the manager of Norwegian club Molde, who he has led to two successive title triumphs.
Quinton Fortune was most recently spotted as a ITV4 studio pundit for their African Nations Cup coverage. The South African played for Bolton, Brescia and Doncaster Rovers after leaving United but retired in 2010. He is currently doing his coaching badges by helping train United's reserve team.
Forlan enjoyed great success after leaving United, more than he ever enjoyed at Old Trafford. He was superb with Villareal in La Liga, going onto win the Europa League with Atletico Madrid. His stunning World Cup 2010 performances earned him a transfer to Inter Milan, and last year he signed for Brazilian club Internacional.
O'Shea left Old Trafford with Wes Brown in 2011, and is an important player for the Black Cats. He will remember the games against Madrid - when he was only a youngster, particularly the return leg where he is best remembered for nutmegging Luis Figo.
Fletcher was a young player on the fringes of breaking through in 2003, and was really only named on the bench because of Juan Veron's injury. He went onto establish himself as a United regular, but his career has been jolted by a bowel illness which has ruled him out for the rest of the season.
United fans, what do you remember about the 3-1 defeat?