The four Premier League clubs have been kept apart in the early stages of the competition but at least one is certain to exit Europe after Liverpool were pitted against Chelsea for a fifth successive year.
Rafa Benitez's Reds, who thumped Real Madrid 5-0 on aggregate in the last 16, will be at home for the first leg of their clash with Chelsea.
The Blues beat Liverpool in the semi-finals last season and have been in fine form since the appointment of Guus Hiddink as manager.
Holders Manchester United will fancy their chances of making it through to the last four after being paired against Portuguese underdogs Porto, with the first leg to be played at Old Trafford.
Arsenal, fresh from beating Roma on penalties, will travel to Villarreal before tackling the Spaniards at Emirates Stadium in the second leg.
In the fourth quarter-final, highly-fancied Barcelona will take on a Bayern Munich side that hammered Sporting 12-1 on aggregate in the last round.
The semi-final draw was also made in Nyon and the winners of the tie between Liverpool and Chelsea will face either Bayern or Barca.
United will face Arsenal in the last four if both sides come through their quarter-finals.
Champions League quarter-final drawVillarreal v Arsenal
Manchester United v Porto
Liverpool v Chelsea
Barcelona v Bayern Munich
Ties to be played on 7th/8th April and 14th/15th April.
Champions League semi-final drawManchester United or Porto v Villarreal or Arsenal
Barcelona or Bayern Munich v Liverpool or Chelsea
Ties to be played on 28th/29th April and 5th/6th May.