Victory over Heineken Cup quarter-final opponents Clermont Auvergne on Sunday would secure a last-four clash for Saracens against Leinster or Cardiff Blues at Twickenham on April 29.
And a sustained presence at the tournament's business end is what McCall desires for a club high on ambition and quality.
"Competing with the elite of Europe in the knockout stages of tournaments is where we want to be - both now and in the future," McCall said.
"If you look at the likes of Toulouse, Leicester, Leinster and Munster, these are teams who have created a legacy in Europe. We want to do the same.
"But we know the size of the challenge in front of us.
"Looking through the Clermont squad, you will see a number of very familiar names from both the club and world stage. It's a massive game and the kind of contest that we relish."
Scrum-half Richard Wigglesworth makes his first start since being injured last October, with England centre Brad Barritt and Wales prop Rhys Gill also returning to a Saracens side captained by Steve Borthwick.
Clermont, though, are seasoned European campaigners, and they have an added incentive of securing a semi-final place for the first time in their history.
"Before I came to France a lot of people thought that the Top 14 was all the French clubs cared about, but it most certainly is not like that now," Clermont's Wales international full-back Lee Byrne said.
"Clermont take the Heineken Cup very seriously, and for the last couple of months the big focus has been on the quarter-final against Saracens.
"The aims of the club this season are to go for the double of Heineken Cup and Top 14, and we feel we have the strength in the squad to have a really good crack at both tournaments."
Before Saracens and Clermont take centre-stage at Vicarage Road, Irish challengers Munster and Ulster will get to grips with each other in Limerick.
And Ulster's attempt to upset the twice European champions has been boosted by Ireland flanker Stephen Ferris recovering from an ankle injury that saw him undergo intensive treatment this week.
"It will be an unbelievably physical battle," Ulster coach Brian McLaughlin said.
"They will be smarting from their defeat to Leinster last weekend, and they will want to make up for that by beating us on Sunday."
And in the second-tier Amlin Challenge Cup on Sunday, the Scarlets head to Brive for a quarter-final encounter that will see the winners book an away tie against Wasps or Biarritz.
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