Domestic league leaders Porto, rivals Benfica and underdogs Braga are all in contention to be at the final in Dublin on May 18.
None of them will meet in the next round after Porto drew Spartak Moscow, Benfica got PSV Eindhoven and Braga were paired with Dynamo Kiev.
However, all three will play their first legs at home and face difficult second-leg away trips.
The fourth quarter-final will see Villarreal face Dutch outfit FC Twente, with the Spaniards at home first.
In the semi-finals, the winner of the Braga-Dynamo clash will be at home first against Benfica or PSV, with Porto or Spartak home first against Villarreal or Twente.
Europa League quarter-finals:
Porto v Spartak Moscow
Benfica v PSV Eindhoven
Villarreal v FC Twente
Braga v Dynamo Kiev
1st legs on April 7, 2nd legs on April 14.
Europa League semi-finals:
Braga or Dynamo Kiev v Benfica or PSV Eindhoven
Porto or Spartak Moscow v Villarreal or FC Twente
1st legs on April 28, 2nd legs on May 5.
