Wasps sit top of the Aviva Premiership, while Leinster lead the way in the Pro12, summing up both side's impressive form so far this term. Leo Cullen's men will be without two of their key Irish internationals, but are in confident mood ahead of playing in front of a partisan home crowd.
"Rob Kearney and Jamie Heaslip are definitely out for the next few weeks, but other than that we're in pretty good shape," said Leinster senior coach Stuart Lancaster.
"Jamie has had an operation on his back, but Johnny Sexton is fit and available.
"Johnny has had some big games for Leinster, even though he's not had a great run of matches this season. When he has played, he has been excellent and I thought one of his best games for us was against Montpellier at the RDS.
"Defensively Wasps are a tough team to play against and in attack they're a real threat. I think we've scored around 79 tries this season and they're very close to that. It's two attack minded teams going head-to-head.
"Both teams have dangerous players, but we need to concede four tries or less to win the game.
"With the Irish players coming back into our side it will add an extra edge to us. To have sold 48,00 tickets for a club match at the Aviva Stadium is incredible really. It's going to be a great occasion, but Leinster have been in this position before. You can see the big players stepping up this week.
"Wasps have a pretty unique way of playing. If we let them have the ball for long periods or turn it over, they will punish you on the counterattack."
Wasps thrashed Leinster twice last season, scoring more than 50 points in the game in Coventry.
This is likely to be a different story, with things expected to be much tighter between two teams boasting a host of international stars.
Lancaster added: "It's important to learn from what happened last year and the mistakes we made to allow those kind of scores. But we are a different team to last year and a lot has happened since then.
"The Aviva is right up there with the most intimidating stadiums in world rugby. We're looking forward to playing there in the first European quarter-final of the weekend.
"Hopefully we can set the benchmark for the other teams to follow."
Dai Young's Wasps head to Dublin in fine fettle and intent on making another semi-final.
Last year's competition saw the Ricoh Arena outfit lose to eventual winners Saracens in the last four, but this season they have a host of star players in excellent form.
England pair Joe Launchbury and Elliot Day are just two of those.
Wasps captain Launchbury said: "We've got a squad who have worked extremely hard to get into this position. We've got ourselves out of a very tough pool, there were times when we weren't favourites to get out of it, so we want to do ourselves justice now.
"Leinster have obviously got some key players in their team. They have quality throughout. You look at a player like Johnny Sexton and the influence he has on a team. For us as a team it's more exciting than anything else. It's a chance for us to go out there on a big stage and show what we can do.
"We've worked hard to get ourselves here, we've had a few big games over the last couple of years that we can draw on as experience and we want to keep having these big games.
"To go to the Aviva and get a win would be huge for us."
- This will be the eighth meeting between the clubs in the European Cup. Wasps hold the head-to-head advantage having won four of the previous seven (D1, L2).
- Wasps won both pool stage matches against Leinster last season, and their 51-10 victory at the Ricoh Arena remains Leinster's heaviest European defeat.
- Leinster won their three home games in the pool stage by an average margin of 40 points, while Wasps won just one of their three away games (D1, L1, won v Zebre).
- Saturday will be Wasps' 100th fixture in the European Cup (W63, D3, L33). The 2004 and '07 winners are the 12th club to reach a century of matches.
- Leinster scored the most tries and points in the pool stage with 31 and 227 respectively, and their captain, Isa Nacewa, is the leading try scorer with six.
- This is the seventh time Wasps have reached the knockout stage.
- Leinster have qualified for the knockout stage for the 12th time (W7, L4) and have won five of their last six quarter-final matches.
- The three-time champions won all 35 scrums on their own feed in the pool stage, and were the only side with 100% success rate. Wasps, by contrast, had the lowest scrum success rate (81%).
- Of the 72 players to make 40+ carries in the pool stage only Montpellier's Nemani Nadolo (9.6) had a better average gain per carry than Wasps' Josh Bassett (8.8 metres).