Manchester United will face European debutants Granada in the quarter-finals of the UEFA Europa League and cannot now meet Arsenal until the final.
The draw for the last eight on Friday (AEDT) kept the two remaining Premier League giants apart.
United claimed a 1-0 win at Milan on Friday to advance 2-1 on aggregate and their reward is La Liga's Granada, winners over Molde.
If United advance, they could have a replay of the 2016-17 final in which they defeated Ajax, who take on Roma.
Ajax were too strong for Young Boys, while Roma dumped out Shakhtar Donetsk.
Arsenal, who knocked out Olympiacos despite losing at home, will be wary of their quarter-final opponents Slavia Prague.
Slavia have already eliminated Leicester City and Rangers, and have now been paired with the 2018-19 finalists, visiting Emirates Stadium before hosting the reverse fixture.
Arsenal's half of the draw is completed by Dinamo Zagreb and Villarreal.
Dinamo defeated Tottenham in a stunning second-leg comeback and could get the chance to complete a north London double if they meet the Gunners.
A meeting between Arsenal and Villarreal would also have significance, with the Spanish outfit coached by Unai Emery, Mikel Arteta's predecessor and a three-time Europa League winner with Sevilla.
Emery's men swept aside Dynamo Kiev in the last 16.
Granada v Manchester United
Arsenal v Slavia Prague
Ajax v Roma
Dinamo Zagreb v Villarreal
Winner of QF 1 v Winner of QF 3
Winner of QF 4 v Winner of QF 2