The English quarter-finalists are two of only four teams, along with Leinster 'A' and Ulster Ravens, who went through the pool stages unbeaten.
The Green & Whites finished Pool 6 a single point behind the Ulstermen, who will have home advantage in their crunch clash with provincial rivals Munster 'A' in the New Year.
Leinster 'A' are the third Irish side to reach the last-eight and will host Welsh Premiership outfit Pontypridd, who finished top of their group with wins over Leeds Carnegie and Swansea.
In the fourth quarter-final Llanelli travel to Cross Keys, the home side securing their path to the knockout stages in their debut year in the competition.
2011/12 BRITISH & IRISH CUP QUARTER-FINALS:
ULSTER RAVENS v MUNSTER 'A'
LEINSTER 'A' v Pontypridd
Cross Keys v Llanelli
All matches to be played over the weekend of January 20-22
Quarter-Final Qualification -
5.2.2 - The six pool winners shall be ranked 1-6 and the runners-up shall then be ranked 7-12, in each case based on their playing record in the pool Stages using 5.2.1 (a)-(j). Those teams ranked 1-8 shall proceed to the quarter-finals.
5.3.3 - The draw for the quarter-final matches shall be made from the teams ranked 1-8 as set out in regulation 5.2.2. Those teams ranked 1-4 in accordance with 5.2.2 will have the home advantage. The draw will be organised by the Committee and will ensure that there are no fixtures that replicate the pool matches.