After signing star players like Zlatan Ibrahimovic and David Beckham, PSG is anxious for a major victory that would justify its engorged payroll and catapult the French team into the upper echelon of the continent's elite.
Standing in its way is Lionel Messi and Barcelona, which is seeking to add to its three Champions League titles in the past seven years.
Also in the last eight on Tuesday, Bayern Munich hosts Juventus in a clash of former champions. On Wednesday, nine-time winner Real Madrid hosts Galatasaray while Borussia Dortmund visits newcomer Malaga.
PSG's Qatari owners have so far seen little return on their massive investment of €260 million ($339 million) on players during the past two seasons, with the squad still yet to gel as a unit under coach Carlo Ancelotti.
Barcelona, on the other hand, has long established itself as the model to follow thanks to its attractive passing game and reliance on homegrown talent that has brought every major title in recent years.
PSG' 23-match unbeaten run at home in European competitions will be tested by Messi, who has scored in a record 19 straight Spanish league games and netted a double to lead Barcelona to an historic comeback win over AC Milan in the last 16.
"We are very motivated to play this game," Messi said. "We need to rest up so we can arrive in the best physical condition and try to get a good result and, if it is possible, to win — even though we know that it will be an evenly fought match from the looks of it."
Coach Tito Vilanova plans to make his return to Barcelona's touchline at the Parc des Princes after a 10-week stay in a New York hospital to receive treatment after having a throat tumour removed in December. The Catalan club will also be boosted by playmaker Xavi Hernandez and left back Jordi Alba returning from injury.
"I've already played against Barcelona since I left the club and I think it's a special match for everyone," said Ibrahimovic, who spent one tumultuous season with Barcelona in 2009-10. "How do you beat them? Good question. I think we will have to concentrate on our way of playing and the coach will choose the right tactics for this match against, without doubt, the best team in the world."
Despite resting some starters, Bayern Munich thrashed Hamburger SV 9-2 — the most lopsided Bundesliga win in 13 years — to place one hand on the domestic trophy on Saturday. But Italian leader Juventus is certain to provide a sterner test.
"Juventus is going to be a very different story, they are a different calibre," said Bayern midfielder Bastian Schweinsteiger, who described the visiting side as "one of the best teams in Europe."
With the German title effectively decided, manager Jupp Heynckes opted to rest several players against Hamburg, with Thomas Mueller, Franck Ribery and Mario Mandzukic all on the bench.
While four-time winner Bayern lost last year's final at home to Chelsea and also finished runner-up in 2010, Juventus is in the quarterfinals for the first time since it was relegated to Serie B due to the 2006 match-fixing scandal.
"We are going to play in Munich with joy and without fear," Juventus coach Antonio Conte said. "We are facing a strong Bayern side, but continue to embrace this dream.
"This double challenge will show us who we are in Europe and at what point we are at in respect to the big clubs in European football. In Italy we realized that we are on the right track and now we want to measure ourselves against Europe, too."
Madrid welcomes Galatasaray with its focus on winning an elusive 10th European Cup.
Madrid coach Jose Mourinho will be pitted against two of his former players in striker Didier Drogba and midfielder Wesley Sneijder, both of whom were recent veteran reinforcements for the Turkish team.
The game will feature the competitions' two top scorers, with Madrid's Cristiano Ronaldo and Galatasaray's Burak Yilmaz both having scored eight goals so far. Messi is next with seven.
Dortmund may have disappointed in the German league this season, but it won its group ahead of Madrid, leaving Manchester City out of the knockout rounds.
Malaga coach Manuel Pellegrini is looking to repeat his feat of leading Villarreal to the semifinals in its first appearance in Europe's top-tier tournament in 2006.