Top favourites Liverpool face Atalanta in the Europa League quarter-finals while West Ham United face German opposition again in the form of unbeaten Bayer Leverkusen.
Should Jürgen Klopp's Liverpool, who have already won the League Cup this term and thrashed Sparta Prague 11-2 from two last 16 legs, progress their striker Darwin Nunez could face former club Benfica.
The Lisbon club was drawn to face Olympique Marseille first in a duel of three-time finalists.
Last year's Conference League winners West Ham ousted Freiburg in the last 16 with the help of a resounding 5-0 thrashing on Thursday, but could face a tougher task against Xabi Alonso's Leverkusen who are unbeaten in all their 37 season games to date.
But it took two stoppage time goals from Patrik Schick against Qarabag to progress and keep the streak alive for the 1988 UEFA Cup champions Leverkusen on Thursday.
The winner faces Italian opposition as AC Milan were drawn to face a Serie A rival yet again in the form of last year's runners-up Roma, a year after first beating Napoli and then losing to Inter in the Champions League knock-outs.
The quarter-finals are April 11 and 18, the semis May 2 and 9, and the final in Dublin on May 22.
The draw at the UEFA headquarters in Nyon was fully open, without country, group stage or seeded teams protection like for the round of 16.
It was also the last draw in the current format as all European competitions will undergo an overhaul to a league format from next season onwards.
