Manchester United have been drawn against Granada in the Europa League quarter-finals, while Arsenal will face Slavia Prague.
Ajax have been drawn against Roma, while Dinamo Zagreb will take on Villarreal.
If Manchester United overcome Granada in the quarter-finals, they will play the winners of the tie between Ajax and Roma.
The victors from Arsenal versus Slavia Prague play either Unai Emery's Villarreal or Zagreb, who stunned Tottenham in the last 16 with a comeback 3-2 aggregate win - meaning an all-Premier League final is possible.
Round of 16 first-leg matches will be played on Thursday April 8, and the second legs will take place the week after, on Thursday April 15. The Europa League semi-finals will be played on April 29, (first leg) and May 6 (second leg). The final will then be played on Wednesday May 26, with the Gdansk Arena in Poland hosting.