United lead Chelsea by six points in the race for the English League title, while both have FA Cup semi-finals ahead, but on Wednesday United face AS Roma in the first leg of the Champions League quarter-finals in Italy while Chelsea take on Valencia at Stamford Bridge.
Good results for both would increase the chances of them advancing to the semi-finals and possibly meeting each other in the finals of both the Champions League and FA Cup.
United probably have the tougher task as they are away in the Italian capital and have never performed particularly well in Italy having lost eight of the 11 matches they have played there and won just twice -- against Juventus (3-2) in 1999 and against Juventus again (3-0) in 2003.
They are currently in fine form though, having played superbly in the second half to beat Blackburn Rovers 4-1 on Saturday, their seventh successive league victory.
Roma, who drew 1-1 with AC Milan at the weekend, will take great heart from their victory over fancied Olympique Lyon in the last round.
Some spice has been added to the occasion with the Mayor of Rome Walter Veltroni unhappy with a letter United sent to its travelling fans warning them they could be attacked by Roma's "ultra" fans and to take extra care while in the Italian capital.
Roma captain Francesco Totti has warned United manager Alex Ferguson he "will remember my name in future" after Ferguson failed to include him in a list of Roma's most dangerous players in a pre-match interview last week.
VIDEO NASTY
Matters appear no more straightforward before Chelsea take on Valencia in London.
Chelsea's Portuguese coach Jose Mourinho has shown his players a video of Valencia's match against Inter Milan in the previous round which ended in a brawl.
Mourinho says he has warned his men to beware of the "Latin mentality" and to keep their composure.
Valencia will be without defender David Navarro, suspended for eight months for his part in the fighting against Inter, while Valencia skipper Carlos Marchena starts his four-match European suspension for his role in the fracas.
Valencia will also be without striker Fernando Morientes (shoulder injury), leaving David Villa as the key striker.
Villa said on Tuesday their confidence was "sky high" for the match.
The English champions have recalled left back Wayne Bridge to the squad after knee surgery and Joe Cole has recovered from the broken foot that kept him out since November but Mourinho has yet to decide on the timing of the midfielder's comeback.
However, they will be without Dutch winger Arjen Robben (knee) and holding midfielder Michael Essien (knee).
Wednesday's quarter-finals follow Tuesday night's matches in which Liverpool won 3-0 at PSV Eindhoven and AC Milan and Bayern Munich drew 2-2 in Milan.
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