helped Manchester United defeat Bayern Munich 2-1 in the 1999 final although they will be without leading scorer Zlatan Ibrahimovic who is suspended for the first-leg at the Parc des Princes.
Lionel Messi will lead four-time champions Barcelona after the Argentine superstar scored twice and inspired the 4-0 thrashing of AC Milan on Tuesday that overturned a 2-0 deficit.
"I think it's brilliant to play Barcelona. I'm very happy but it'll be very difficult... Barca have a lot of experience, quality and confidence but PSG have a chance of going through. We'll have to play the full 180 minutes," said Paris Saint-Germain's Italian coach Carlo Ancelotti.
PSG sporting director Leonardo also focussed on the daunting prospect of playing a team widely recognised as the best in club football.
"It's the toughest draw we could get and it's going to be difficult," said the former PSG player.
"It's not going to be easy but the two matches will bring us a lot of enjoyment and they will be great matches of football," added the Brazilian.
Last year's losing finalists Bayern Munich, will play the first-leg at home against Italian giants Juventus, while record nine-time champions Real Madrid will take on a Galatasaray team attempting to become the first side from Turkey to lift the trophy.
"They are an opponent with a lot of calibre and they are very, very strong," said Bayern coach Jupp Heynckes who won the trophy with Real Madrid in 1998, but is set to leave at the end of the season and make way for Pep Guardiola.
"It's going to be two great nights but I know Juventus very well and they are currently the best team in Italy with a very strong defence and plenty of offensive quality too.
Bayern midfielder Bastian Schweinsteiger - who cut a distraught figure after missing the penalty that cost his side the trophy in last year's final against Chelsea - also paid tribute to the Serie A leaders.
"They are a very, very good team with some great players such as (Andrea) Pirlo."
"That is certainly not a dream draw for us," was the reaction of Bayern chief executive Karl-Heinz Rummenigge.
"Statistically we have not had good experiences with Juventus. It will be difficult and we will need to play two good matches, be well organised and make no mistake if we want to reach the semi-finals."
Jose Mourinho continues his quest to become the first coach to win the tournament with three different teams after Porto in 2004 and Inter Milan in 2010 but former Real Madrid striker Emilio Butragueno expects a tough battle.
"Galatasaray are a great team and have fantastic fans so we are expecting two tough matches," said the former Spanish international.
"They have some great players like (Wesley) Sneijder and (Didier) Drogba but our objective is to win that 10th European Cup. That is our goal," he added.
In the final quarter-final, Spanish outsiders Malaga were drawn against 1997 champions Borussia Dortmund with the first-leg to be played in Spain.
"We can live with this draw," Dortmund sports director Michael Zorc said. "At least it is better than playing Barcelona, Real or Bayern."
The final is set for Wembley on May 25 although there are no English clubs remaining in the last eight for the first time since 1996, while defending champions Chelsea failed to make it out of the group stages.
Champions League quarter-final draw:
Matches to be played on April 2/3 and April 9/10
Paris Saint-Germain (FRA) v Barcelona (ESP)
Malaga (ESP) v Borussia Dortmund (GER)
Real Madrid (ESP) v Galatasary (TUR)
Bayern Munich (GER) v Juventus (ITA)