United will go up against Bayern, a repeat of the 1999 final. Sir Alex Ferguson's men beat the German giants in dramatic fashion at the Nou Camp 11 years ago, scoring twice in the dying minutes to complete an historic Treble.
United thrashed AC Milan in the previous round and will be confident of progressing to the semis, where they will face the winner of the all-French clash between Lyon and Bordeaux.
United will be at home in the second leg, but Arsenal are at home first to Barcelona.
Arsenal boss Arsene Wenger will no doubt have wanted to avoid Barca, but Cesc Fabregas will relish playing against his former club, with whom he is often linked with a return. The tie also sees Gunners legend Thierry Henry take on his former employers.
The winner of that tie will face either Jose Mourinho's Inter Milan - who knocked out Chelsea earlier this week - or CSKA Moscow in the semi-finals.
Quarter-finals: First-leg ties:
Tuesday March 30: Bayern Munich v Manchester United, Lyon v Bordeaux.
Wednesday March 31: Arsenal v Barcelona, Inter Milan v CSKA Moscow.
Tuesday April 6: Barcelona v Arsenal, CSKA Moscow v Inter Milan.
Wednesday April 7: Manchester United v Bayern, Bordeaux v Lyon.
Semi-finals: First-leg ties:
Tuesday April 20: Inter Milan or CSKA Moscow v Arsenal or Barcelona.
Wednesday April 21: Bayern Munich or Manchester United v Lyon or Bordeaux.
Tuesday April 27: Lyon or Bordeaux v Bayern Munich or Manchester United.
Wednesday April 28: Arsenal or Barcelona v Inter Milan or CSKA Moscow.
The final will take place at the Bernabeu stadium in Madrid on Saturday, May 22.
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