The two-legged ties will be played from February 16.
Both sides had shots cleared off the line but Real were left feeling more disappointed after winning the tactical battle but failing to take their chances.
Suarez had joined Barcelona in 2014. He scored 198 goals in 283 games for the Catalan side and he also earned the Golden Shoe as Europe's top scorer after scoring 59 total goals in 2015-16.
'A ridiculous goal conceded from a corner will be the epitaph of this team, which repeated the mistakes of Rome'
The Argentine's representatives and Barcelona did not immediately respond to requests for comment.
Images from La Liga matches played on Monday.
Angry Barcelona fans chanted for the resignation of the club president Josep Maria Bartomeu after captain Lionel Messi announced on Tuesday that he wished to leave the Catalan side.
The Dutchman burst through the middle of the pitch and laid the ball off for Messi to dribble into the net for an 18th league goal of the season, extending his lead at the top of the scoring charts.
Barcelona announced the signing of Griezmann this month for 120 million euros
Barcelona are taking measures to cut the wages of their players and staff to reduce the economic effects of the coronavirus crisis, the La Liga club said on Thursday. All professional players at Barcelona, including six-times world player of the year Lionel Messi, as well as non-playing staff, will face a compulsory wage reduction during the period of lockdown, the club's directors decided at a board meeting held via video conference.
A round-up of Wednesday's action in the UEFA Champions League.
Messi's damning assessment of the team came home to roost when the season re-started after the coronavirus stoppage and Barca surrendered the league title to Real Madrid, prompting the captain to launch a new tirade against the team.
Images from Sunday's action in La Liga and Ligue 1.
Barcelona's last Champions League triumph came in 2015, and since then they have failed to get beyond the quarter-finals while Real Madrid have monopolised the trophy.
According to Goal.com, Messi was set to return to the Catalan capital with his family at the weekend, but will now not be back until around July 12.
Lionel Messi became Barca's record appearance maker in the competition with 76 Copa matches.
Pope Francis is known to be a football fan, and he is also a club member of Buenos Aires side San Lorenzo.
A summary of Thursday's second leg quarter-final matches in the Europa League.
'I would never go to court against Barca because it is the club that I love, which gave me everything since I arrived. It is the club of my life, I have made my life here.'
Spain striker Iago Aspas dealt a fresh blow to Barcelona's La Liga title hopes by striking a late free kick to snatch a 2-2 draw at home to the Catalans on Saturday as Quique Setien's side twice threw away the lead in a thrilling match. The draw put Barca back on top of the table on 69 points after 32 games but Real Madrid, on 68, can go two points clear at the summit if they beat Espanyol away from home on Sunday.
Barcelona president Josep Maria Bartomeu's remarks come amid severe speculation around Messi's future at the club.
Impressive performances from Lionel Messi and Ansu Fati helped Barcelona overcome an early red card to defender Clement Lenglet and win 3-0 at Celta Vigo on Thursday to make it two wins out of two in the new La Liga season.
La Liga champions Barcelona's domestic struggles continued as they dropped points for the third game in a row, drawing 1-1 at home to Athletic Bilbao on Saturday after Lionel Messi and Sergio Busquets had begun the match on the substitutes' bench.
Barcelona have joined captain Andres Iniesta in calling for dialogue between the Spanish government and leaders in Catalonia to resolve the crisis between the central government and its richest region following Sunday's disputed referendum.
Barcelona president Josep Maria Bartomeu resigned from the club on Tuesday ahead of a vote of no confidence that was due to be held next month after some 20,000 fans signed a petition demanding that he step down.
PSG have set their sights on Messi, with PSG's players, coaches talking of their excitement about the prospect of bringing the Argentine to the French capital
Jenni Hermoso scored a late hat-trick as Barcelona hammered CD Tacon 9-1
Real Madrid will sack Santiago Solari and reappoint former coach Zinedine Zidane on Monday, according to multiple Spanish media reports.
Zinedine Zidane's side joined Atletico Madrid on 66 points and moved top of the table
Italy's top-flight Serie A soccer league launched a new anti-racism campaign on Monday by presenting artwork featuring three side-by-side paintings of apes but the move has been described by campaign group Fare as a sick joke. News of all that's transpired on and off the football field.
Following his debut, Messi made just eight more appearances for the first team that season.
A summary of all things football.
Real Madrid captain Sergio Ramos once again proved to be the man for the big occasion as he converted a fiercely debated penalty to help his side to a 3-1 win over rivals Barcelona at an empty Camp Nou in La Liga on Saturday.
France forward Griezmann, 28, rejected a move to Barcelona last year but announced in May he was leaving the Madrid side, where he has spent the last five seasons since signing from Real Sociedad in 2014.
News of all that transpired on and off the football field...
La Liga leaders Barcelona beat Real Madrid 1-0 to all but knock their rivals out of the title race on Saturday, while second-placed Atletico Madrid stayed seven points behind the Catalans with a 2-0 win at Real Sociedad on Sunday.
News of all that's transpired on and off the football field.
Real and Barca have won the title in 15 of the last 16 seasons, with Atletico breaking the duopoly in 2014.
The win took Barca to the top of the standings on 68 points although Real Madrid, on 65, will reclaim their lead due to their superior head-to-head record if they beat Real Mallorca at home on Wednesday.
Barcelona is reportedly looking to buy ManchesterCity star David Silva as a replacement for their veteran star midfielder Xavi.