The other three ties are also delicately poised in a competition which is often dismissed as the poor relation to the Champions League but which this year has featured some outstanding games in the knockout stages.
English side Fulham, playing in the quarter-finals of a European competition for the first time, take a 2-1 lead to German champions VfL Wolfsburg determined to continue a run which has captured the imagination of their supporters.
Liverpool trail 2-1 from the first leg as they host Benfica in a clash of two former European champions, as do Standard Liege who entertain a Hamburg SV team where frustrations are starting to boil over.
Valencia, held 2-2 at home by Atletico last week, find themselves in a similar position to the previous round, when they drew 1-1 at home to Werder and went through on away goals after an eight-goal thriller in the return.
"We did it the difficult way in Germany and we are capable of repeating that in Madrid," playmaker David Silva told UEFA.com.
"Playing Atletico felt very similar to the first leg against Werder because of the opportunities we didn't convert. The Calderon is a difficult place to try to win, but if we create as many chances as we did in Germany, then we'll do it.
"We will travel with confidence in our ability and we will show pride."
Valencia are hoping for another inspired performance from Spain's World Cup-bound striker David Villa, whose 27 goals in all competitions this season included a stunning hat-trick at Werder and a late equaliser in the first leg against Atletico.
LEAGUE PRIORITY
The match at Anfield will feature two of the teams who appear to be least excited about the competition.
For Liverpool, the Europa League - the rebranded version of the UEFA Cup which they won three times - is a mere consolation in a season where they exited the Champions League at the group stage and dropped out of the Premier League running by January.
Their opponents are more interested in winning the Portuguese Super League for the first time since 2005, having seen their bitter rivals Porto walk off with the title in the subsequent four seasons.
"Our main goal is to win the national championship," Benfica coach Jorge Jesus, whose team will be without former Argentina forward Javier Saviola due to a foot injury, told reporters.
Fulham, on the other hand, are delighted to be involved, having reached the last eight at the expense of Juventus.
"It is huge what we have already accomplished for the club and as players we want to continue it," said goalkeeper Mark Schwarzer.
"You need to ask the chairman and the fans how big an achievement they think it is, but as players we are on the verge of something huge."
Hamburg, whose stadium hosts the May 12 final, could certainly do with a boost.
