Top seeds Northampton will host Irish province Ulster in the quarter-finals of the Heineken Cup and will also have home advantage if they reach the semis.
Saints, who won all six of their group games, may have to switch their last-eight tie from Franklin's Gardens to a stadium with a minimum 15,000 capacity.
Two-time champions Leicester have to travel to face 2009 champions Leinster, with the winners at home in the semis.
Perpignan play Toulon and Biarritz host Toulouse in two all-French ties.
The latter is a repeat of last year's final, when Toulouse clinched their fourth title with a 21-19 victory over their rivals in Paris.
There is also a mouthwatering repeat of the 2009 final, with Leinster - who qualified as second seeds - hosting Leicester in Dublin.
Toulouse looked set for a home quarter-final until a last-minute try from Wasps wing David Lemi saw them beaten in High Wycombe in Sunday's final round of pool fixtures.
Victory for Wasps, who finished runners-up behind Toulouse in their pool, sent them into the second-tier Amlin Challenge Cup, where they will face local rivals Harlequins in the last eight.
Two-time Heineken champions Munster, who failed to qualify for the knock-out stages of the elite tournament for the first time in 13 years, have an away tie in Brive.
The other two matches are all-French affairs, with Stade Francais hosting Montpellier and La Rochelle facing Clermont Auvergne.
The quarter-finals of both competitions will be played on the weekend of 8/9/10 April, with the semi-finals on the weekend of 30 April/1 May. The Heineken Cup final takes place in Cardiff on 21 May, with the Challenge Cup final the night before, also in the Welsh capital.
Heineken Cup quarter-finals:
Northampton v Ulster
Leinster v Leicester
Perpignan v Toulon
Biarritz v Toulouse
Heineken Cup semi-finals:
Leinster/Leicester v Biarritz/Toulouse
Northampton/Ulster v Perpignan/Toulon
Amlin Challenge Cup quarter-finals:
Stade Francais v Montpellier
Brive v Munster
La Rochelle v Clermont Auvergne
Harlequins v Wasps
Amlin Challenge Cup semi-finals:
Stade Francais/Montpellier v La Rochelle/Clermont Auvergne
Brive/Munster v Harlequins/Wasps