Saracens will then take on last season's beaten finalists Ulster in the second of the Saturday fixtures with the venue to be announced at a later date.
It is thought Saracens are exploring their new Allianz Park home in Barnet as a possible location, although Milton Keynes' Stadium:mk could be another option.
Sunday's two matches on 7 April will kick off with the showdown between Harlequins and two-time former Heineken Cup champions Munster at the Twickenham Stoop.
French heavyweights Toulon then host Leicester, who won the tournament in 2001 and 2002, in the first ever meeting between the clubs in Europe, with the venue still to be confirmed.
Saturday's two matches will be broadcast live on Sky Sports 1 HD, with Sunday's action switching to Sky Sports 2 HD.
Saturday 6 April:
ASM Clermont Auvergne v Montpellier, Stade Marcel Michelin, 15.40
Saracens v Ulster Rugby, Venue TBC, 18.30
Sunday 7 April:
Harlequins v Munster Rugby, Twickenham Stoop, 14.00
Toulon v Leicester Tigers, Venue TBC, 16.30
Amlin Challenge Cup quarter-finals:
Thursday 4 April:
Gloucester v Biarritz, Kingsholm, 20.00
Friday 5 April:
Wasps v Leinster, Adams Park, 20.00
Perpignan v Toulouse, Stade Aime Giral, 19.00
Saturday 6 April:
Bath v Stade Francais, Recreation Ground, 13.00
Source : http://www1.skysports.com/rugby-union/news/12552/8430468/Heineken-Cup-quarter-final-dates-confirmed
