This week's clash will be the first time that the domestic rivals have met in a UEFA competition, but they have faced off on 158 occasions in the league and Spanish Cup, with Sevilla just shading the head-to-head record.
With the winner of the Europa League advancing immediately into the group stages of next season's Champions League, Bilbao will be desperate to land the crown this term. They are currently nine points off the top four in La Liga - making qualification for Europe's premier competition through their domestic position unlikely - but overcoming Sevilla to reach the semi-finals would leave them within touching distance of the final.
Ernesto Valverde's side topped Group L with 13 points to advance into the round of 32, where they beat French outfit Marseille 2-1 on aggregate. The Basque outfit were then paired with Gary Neville's Valencia and despite losing the second leg 2-1 at the Mestalla, Bilbao progressed to the quarter-finals on away goals.
Bilbao are actually unbeaten in seven European home matches this season - winning five times in the process. They might have never won the UEFA Cup/Europa League, but the Spanish side have reached the final on two occasions, the last of which was in 2012, when they were beaten 3-0 by Atletico Madrid.
Valverde's side have also won both of their home games against Spanish opposition is Europe and have been victorious in their last three matches at San Mames in all competitions. There are some impressive teams left in this season's Europa League, but the victor of this quarter-final might well fancy their chances of claiming the title.
That said, Bilbao have actually lost two of their last three games in all competitions and will enter the match off the back of a disappointing 1-1 draw at home to Granada on Sunday. They have this season's Europa League top scorer in their ranks, however, with Spanish international Artiz Aduriz netting eight goals in the competition this term.
Recent form: WDWDWL
Recent form (all competitions): WWWLLD
Having won Europe's second competition on four previous occasions - 2006, 2007, 2014 and 2015 - Sevilla are searching for a fifth European crown this season and their third in a row. The Europa League has been kind to Unai Emery's side in recent years and their credentials in this tournament have seen them placed among the favourites at this stage.
Unlike Bilbao, Sevilla started this season in the Champions League following their Europa League success last term, but the Spanish outfit could not find a route through Group D. In truth, it was a really tough ask for the third seeds, who were drawn alongside Manchester City and Juventus. They did win two of their six group matches, but four defeats saw them finish third and drop into the competition where they feel most comfortable.
A 3-1 aggregate victory over Molde saw Emery's side progress into the round of 16, where they overcame Basel to set up an all-Spanish quarter-final. They have actually only lost once in the Europa League since November 2014 and have only once been eliminated in the quarter-final stage of a European competition - against Real Madrid in 1958.
Sevilla's 16 European fixtures against Spanish rivals have ended in six wins, three draws and seven losses, and four of those defeats have come on the road. Indeed, the story of Sevilla's campaign has been their dreadful away form, which has really harmed their chances of finishing in the top four in their domestic table.
Incredibly, Sevilla have not recorded a single away victory in either La Liga or Europe this season. They have drawn nine of their 15 on the road in the league and lost four of their five in European action. Their home form, across all competitions, has been excellent in the last couple of years, but they are just not the same team away from the Estadio Ramon.
Sevilla will not enter the match in the best of form, meanwhile, having lost each of their last two in the league. They suffered a 4-0 defeat at Real Madrid on March 20 and also lost 2-1 at Real Sociedad on Sunday. San Mames is a tough place to visit and a poor first-leg result could leave Emery's side with a mountain to climb in the second leg.
Recent form: WWWLDW
Recent form (all competitions): DDWWLL
Sabin Merino is also a slight doubt due to a hamstring problem, which should allow Inaki Williams to return to the XI, alongside Mikel Rico, who should replace the suspended Garcia in an advanced midfield position.
As for Sevilla, Emery has no fresh injury concerns from the weekend, but a hamstring injury will keep Portuguese centre-back Daniel Carrico on the sidelines once again.
Emery's main decision will come in attack, where Gameiro and former Bilbao striker Fernando Llorente are battling for one position. It will be the first time that Llorente has returned to the club that he left on a free transfer in 2013, and the 31-year-old has three European goals to his name this season.
Bilbao possible starting lineup:
Iraizoz; De Marcos, Gurpegi, Etxeita, Balenziaga; Benat, San Jose; Williams, Rico, Susaeta; Aduriz
Sevilla possible starting lineup:
Rico; Coke, Rami, Kolo, Tremoulinas; Krychowiak, N'Zonzi; Vitolo, Banega, Konoplyanka; Gameiro
Head To Head
As mentioned, Thursday will be the first time that these two teams have met in a European match.
They have clashed on 158 occasions in Spanish football, however, and Sevilla currently lead the head-to-head 64-63. Bilbao have an 8-5 lead in cup football, but Sevilla have won 59 to Bilbao's 55 in the league.
The two sides have also met once this season, and it was Sevilla that recorded a 2-0 victory in the league match on January 9 courtesy of a double from French striker Gameiro. The return fixture at the Estadio Ramon will take place on the final weekend of the season.
We say: Bilbao 2-1 Sevilla
Sevilla's terrible away record this season cannot be ignored and it is difficult to see a win arriving at San Mames. Away goals are the name of the game in the knockout rounds and we believe that Sevilla would be more than happy with a narrow defeat, providing that they can find the back of the net. Garcia is a big miss for Bilbao, but in Aduriz and Gameiro, both teams have plenty of goals in the striking positions.