The Barnet ground is the preferred choice for the match, which is to be played on the weekend of April 26-28, with Wembley or Twickenham potential alternatives.
Sunday's test event against Cardiff in the LV= Cup will be the first game played on the artificial pitch in front of a crowd of 3,500, three weeks before the official opening against Exeter on February 16.
Chief executive Edward Griffiths hopes Barnet Council will grant Saracens permission to temporarily increase the 10,000 capacity to 15,000 to comply with tournament organisers European Rugby Cup's rules for hosting quarter-finals.
"There are a number of hoops to go through before we can hold the match at Allianz Park," Griffiths said.
"We are in talks with the council over the capacity to see if it's perfectly possible to increase the capacity for one match, or if it's too soon.
"This is our home ground now so we'd like to stage the match here. This is absolutely our first choice.
"We want to try and bring those discussions to a close by the end of next week. We want something agreed as soon as possible."