Premiership leaders Harlequins will host Munster in the Heineken Cup last eight after qualifying as top seeds.
Saracens will also be at home in the quarter-finals, due to be played on 5-7 April, against Ulster.
Leicester face a difficult trip to play Jonny Wilkinson's Toulon in France.
If Saracens go through their semi-final, potentially against Leicester, will be in England, while Quins or Munster must travel to a French side, with ties to be played on 26-28 April.
Heineken Cup quarter-final draw:
Harlequins v Munster
Clermont Auvergne v Montpellier
Toulon v Leicester
Saracens v Ulster
(ties to be played on the weekend of 5-7 April)
Saracens or Ulster v Toulon or Leicester
Clermont Auvergne or Montpellier v Harlequins or Munster
(ties to be played on the weekend of 26-28 April)