Athletic Bilbao, conquerors of Manchester United, will face German side Schalke in the quarter-finals of the Europa League.
Sporting, who held off Manchester City to clinch their place in the last eight, will play Ukrainian side Metalist Kharkiv.
Bilbao and Sporting could face each other in the semi-finals - their quarter-finals have been paired together.
Two other Spanish sides are also still in the Europa League - Atletico Madrid play German club Hannover in one quarter-final with the winners facing the victors of the other between Dutch side AZ Alkmaar and Valencia.
Klaas Jan Huntelaar scored a hat-trick for Schalke on Thursday night and, as a former Real Madrid player, is aware of the threat Bilbao will pose.
"I remember scoring twice against Bilbao for Madrid," he said. "It was a match we won 5-2.
"But that was a while ago. They are a strong team with good players.
"The key will be how we perform in the opening leg at Schalke."
Hannover coach Mirko Slomko is relishing the match against Atletico.
"It is a very challenging but very exciting draw," he said.
"The Spaniards are one of the favourites for the title. They proved that, among other things, against Lazio (in the last 32)."
Quarter-finals
AZ Alkmaar v Valencia
Schalke v Athletic Bilbao
Sporting v Metalist Kharkiv
Atletico Madrid v Hannover
First legs to be played on March 29
Second legs to be played on April 5
Semi-finals
Atletico Madrid/Hannover v AZ Alkmaar/Valencia
Sporting/Metalist Kharkiv v Schalke/Athletic Bilbao
First legs to be played on April 19
Second legs to be played on April 26
Sporting, who held off Manchester City to clinch their place in the last eight, will play Ukrainian side Metalist Kharkiv.
Bilbao and Sporting could face each other in the semi-finals - their quarter-finals have been paired together.
Two other Spanish sides are also still in the Europa League - Atletico Madrid play German club Hannover in one quarter-final with the winners facing the victors of the other between Dutch side AZ Alkmaar and Valencia.
Klaas Jan Huntelaar scored a hat-trick for Schalke on Thursday night and, as a former Real Madrid player, is aware of the threat Bilbao will pose.
"I remember scoring twice against Bilbao for Madrid," he said. "It was a match we won 5-2.
"But that was a while ago. They are a strong team with good players.
"The key will be how we perform in the opening leg at Schalke."
Hannover coach Mirko Slomko is relishing the match against Atletico.
"It is a very challenging but very exciting draw," he said.
"The Spaniards are one of the favourites for the title. They proved that, among other things, against Lazio (in the last 32)."
Quarter-finals
AZ Alkmaar v Valencia
Schalke v Athletic Bilbao
Sporting v Metalist Kharkiv
Atletico Madrid v Hannover
First legs to be played on March 29
Second legs to be played on April 5
Semi-finals
Atletico Madrid/Hannover v AZ Alkmaar/Valencia
Sporting/Metalist Kharkiv v Schalke/Athletic Bilbao
First legs to be played on April 19
Second legs to be played on April 26