Gaffney's side need to overcome the Ospreys to reach the semi-finals. If they do so, Sarries will have home advantage against either Gloucester of Munster.
During his three-year tenure at Munster between 2002 and 2005, Gaffney guided the province to one quarter-final and two semi-finals in the Heineken Cup.
Meanwhile, first-time quarter-finalists London Irish will be at home to either Toulouse or Cardiff Blues in the first semi-final, provided they can see off the challenge of Perpignan in the last-eight.
The semi-finals will be played over the weekend of April 26-27.
2007/08 HEINEKEN CUP SEMI-FINAL DRAW:
London Irish or Perpignan v Toulouse or Cardiff Blues
Saracens or Ospreys v Gloucester or Munster
Meanwhile, the dates, kick-off times and host broadcasters for the 2007/08 Heineken Cup quarter-finals on April 5-6 have been confirmed. Additional TV details will be announced shortly.
2007/08 HEINEKEN CUP QUARTER-FINALS:
Saturday, April 5 -
London Irish v Perpignan, 3pm (local time) Sky Sports
Gloucester v Munster, 5.30pm (local time) Sky Sports
Sunday, April 6 -
Saracens v Ospreys, 12.30pm (local time) Sky Sports
Toulouse v Cardiff Blues, 4pm (local time) France Televisions