Gloucester will aim to continue their unbeaten run in the Challenge Cup when they host Castres in the last 16.
Top seeds Sharks are the other unbeaten side in the tournament and the South Africans host Zebre.
The qualifiers come from the top four sides in the three pools with Connacht, Ulster, Bayonne and Sale dropping down from the Investec Champions Cup.
Ospreys host Sale Sharks, Ulster travel to face Montpellier, while Pau will entertain Connacht.
All fixtures are to be played on the weekend 5-7 April.
Edinburgh have a home tie against Bayonne, while Lions will travel to face Benetton and Clermont Auvergne entertain Cheetahs.
Ospreys are the only Welsh side to have reached the knockout stages of either European competition.
Dragons, Oyonnax, Newcastle, Perpignan, Black Lion and Scarlets are out after finishing in the bottom two of their pools.
Sharks v Zebre
Gloucester v Castres
Benetton v Lions
Clermont Auvergne v Cheetahs
Montpellier v Ulster
Pau v Connacht
Ospreys v Sale Sharks
Edinburgh v Bayonne
Last 16 – 5/6/7 April
Quarter-finals – 12/13/14 April
Semi-finals – 3/4/5 May
Final – 25 May.