But they will have to do what no other side has done in the competition and beat Saracens at Allianz Park. Around 15,000 fans will be packed into the North London Stadium to watch Owen Farrell and co. take on the former Guinness PRO12 champions. And head coach McCall is wary of the Warriors' threats.
"We're playing against a really good opponent this week," he said. "I think Glasgow Warriors were probably the best team in the pool stages of the competition. They put together some really credible wins, they showed they are well coached and they've got players who are very confident at the moment.
"We've just got to keep our feet on the ground and have the same sort of preparation we just had. Hopefully if we can replicate what we showed in the last half an hour of Sunday's match we'll be tough to beat."
Saracens will have Billy and Mako Vunipola available after they came through the thumping 53-10 Premiership triumph over Bath Rugby last weekend. But with the likes of RBS 6 Nations player of the year Stuart Hogg in their ranks, Glasgow will be confident of upsetting the odds.
Jonny Gray also starred for Scotland as they enjoyed a successful RBS 6 Nations championship. And head coach Gregor Townsend has warned his charges they face the ultimate challenge this weekend.
He said: "Saracens have become our role model - in the way they've built a winning rugby culture with such consistency. We've been looking closely to find ways we can beat them. But we know how good they are because they haven't lost a game in Europe for two years.
"They've got a real clarity about their play and the Vunipola brothers are back and maybe George Kruis too. But we play outstanding teams like Munster and Leinster in the Pro 12 and in Europe this season we've beaten Racing and Leicester home and away. This will be the ultimate challenge but we go there with confidence and could take 6,000 fans."
- The clubs have met twice before in the European Cup with Saracens winning both pool stage matches in 2007/08. They also met in the 2007 Challenge Cup quarter-final with the Premiership side winning again on that occasion.
- Saracens have won their last 12 home games in the tournament, with their last four defeats at home all coming against TOP 14 opposition.
- Glasgow have lost 16 of their 18 away games against Aviva Premiership opposition, however, their two victories in that time have come in their last four trips, including Round 6 this season when they inflicted a record 43-0 defeat on Leicester Tigers at Welford Road.
- This is the seventh time Saracens have reached the quarter-finals and the sixth season in a row.
- Glasgow have reached the knockout stage for the first time in their history, and they are the 34th club to achieve the feat.
- Saracens were one of just three sides to manage success rates of 90% + at both lineout (93%) and scrum (90%) during the pool stage (also Toulon and Leinster).
- Last season's EPCR European Player of the Year, Maro Itoje, didn't miss a tackle in the pool stage, completing all 47 he attempted. Only Tom Palmer (53) of Bordeaux-Bègles attempted more without missing at least one.
- The two players to make the most tackles during the pool stage were Glasgow's Jonny Gray (76/80) and Ryan Wilson (70/81).
- Chris Ashton's try in Saracens' win over Toulon moved him past Brian O'Driscoll's total on the all-time list to 34, and he is now just two behind Vincent Clerc on 36.
- Owen Farrell, who made his 50th tournament appearance for Saracens against Toulon, was the pool stage top points scorer with 79 and his overall total of 549 points puts him sixth on the all-time list.