While Bayern, the German champions-elect, face Juve, the Italian champions-elect, in Munich buoyed up by a 9-2 win over old rivals SV Hamburg on Saturday, tournament favourites Barcelona and Paris St Germain, two more teams set to be crowned domestic kings soon, have an intriguing first-leg tie in the French capital.
Real Madrid host Turkish league leaders Galatasaray while the surprise survivors and Spain's third team Malaga are at home to Borussia Dortmund, who are about to lose their Bundesliga title to Bayern but are still contenders in this competition.
Five of the quarter-finalists are far ahead of their rivals in their own leagues and look set to finish as domestic champions long before the end of the season - enabling them to concentrate their efforts on Champions League success if they advance to the last four.
Bayern are 20 points clear of Borussia in Germany and would have been crowned champions on Saturday, after their staggering demolition of former European champions Hamburg, until Robert Lewandowski scored a late goal to give Dortmund a 2-1 win at VfB Stuttgart.
Juventus beat Inter Milan 2-1 on Saturday to move 11 points clear of AC Milan at the top of Serie A, while Barcelona are 13 points clear of Real Madrid in La Liga.
Galatasaray and PSG hold comfortable leads in Turkey and France respectively, and, while Real and Dortmund have no realistic chance of retaining their titles, they are guaranteed to finish high enough to be back in the Champions League next season.
Despite the absence of any English Premier League teams in the last eight for the first time since 1996, this year's final in London could feature a "Clasico" between Real and Barca or an all-German final between Borussia and Bayern.
The quarter-final draw kept alive those prospects at the same time as serving up four intriguing last-eight ties which kick off on Tuesday when Bayern host Juventus and PSG play Barcelona.
Bayern, last season's losing finalists, squeezed into the last eight on away goals after beating Arsenal 3-1 in London before a surprise 2-0 home defeat in the second leg, but they showed that aberration was behind them on Saturday.
Peruvian striker Claudio Pizarro scored four with Dutchman Arjen Robben adding two more in a dazzling performance that will put Juve on full alert.
Bayern coach Jupp Heynckes said: "We played textbook football at times today and the title cannot really slip away any more.
"It was important to fill up on confidence but Tuesday's game will be different with Juve being a top European team and much more aggressive."
Juventus though had a good win of their own, with goals from Fabio Quagliarella and Alessandro Matri giving them victory over Inter.
Tuesday's match will be a contrast in styles with Bayern usually favouring a 4-2-3-1 system while Juve play a 3-5-2 style with Andrea Pirlo attempting to orchestrate their attacks from midfield. A classic is on the cards.
PSG, in the quarter-finals for the first time in 18 years, won their only previous Champions League meeting with Barca when they knocked them out 3-2 on aggregate in a quarter-final clash in 1995.
Much has changed since, with PSG notable absentees from the later stages of the tournament while Barca have been crowned European champions three times.
PSG will be looking for ex-Barcelona striker Zlatan Ibrahimovic to be inspired against his former club while David Beckham, the last English player left in the tournament, could be used as an impact substitute in the later stages.
Barcelona bounced back from a 2-0 first-leg defeat to Milan in the last 16 to triumph 4-0 at home and qualify with some ease in the end, and, with the irrepressible World Player of the Year Lionel Messi in outstanding form, Barca look to have the edge.
Messi scored for the 19th successive league match against Celta Vigo on Saturday in a 2-2 draw to take his league tally for the season to 43. His former Barca team mate Thiago Motta, who could yet prove pivotal for PSG, is just back from injury and likely to be on the bench.
The clash between Real Madrid and Galatasaray brings together more old club mates: Jose Mourinho, Didier Drogba and Wesley Sneijder.
Mourinho is set on leading Real to a record-extending 10th European Cup success while becoming the first man to win the trophy with three different clubs following his earlier successes with Porto and Inter.
Mourinho worked with Drogba at Chelsea and Sneijder was in his Inter team that won the Champions League in 2010, but Sneijder and his new team mates have a tough task ahead of them now.
The tie brings together the two leading scorers in this season's competition who both have eight goals: Cristiano Ronaldo of Real and Burak Yilmaz of Galatasaray. Both scored home and away goals in the last round.
The second legs take place next week, with the semi-finals at the end of April and the beginning of May. The final is at Wembley on May 25.