Arsenal face a tough test against Napoli while Chelsea will take on Slavia Prague in the Europa League quarter-finals.
Unai Emery's Gunners overturned a first-leg deficit to progress at the expense of Rennes on Thursday but will now have to get past Serie A's second-placed side if they are to progress to the last four.
An all-Premier League final in Baku remains a possibility after Arsenal and Chelsea, who will be wary of a Slavia Prague team who knocked out Sevilla in the previous round, were kept apart in the semi-final draw.
In the other quarter-final ties, Villarreal will go up against familiar foes in LaLiga rivals Valencia and Eintracht Frankfurt's reward for ending Inter's European campaign is a clash with Benfica.
Arsenal were initially set to host Napoli in the second leg at Emirates Stadium on April 18 but their fixtures have been switched to make sure they do not play at home on the same day as Chelsea, in accordance with UEFA Club Competitions Committee principles.
After dismissing Dynamo Kiev 8-0 on aggregate, the Blues will travel to Prague on April 11. Maurizio Sarri's side will have home advantage a week later for the return game, though in between they travel to Liverpool in Premier League action.
Relegation-threatened Villarreal are struggling domestically but will hope to upset domestic rivals Valencia, who progressed in dramatic circumstances on Thursday when Goncalo Guedes' injury-time equaliser away to Krasnodar secured a 3-2 aggregate triumph.
Frankfurt sealed their place in the quarters with a 1-0 victory at San Siro, Luka Jovic – who is on loan at the Bundesliga club from future opponents Benfica – grabbing the only goal in the first half.
Europa League quarter-final draw in full:
Arsenal v Napoli
Villarreal v Valencia
Benfica v Eintracht Frankfurt
Slavia Prague v Chelsea