United are favourites to lift the trophy in May and could be dealt a relatively straight-forward draw.
Lyon held their first-leg advantage to knockout Roma while Ajax came from behind to beat Copenhagen. Schalke 04 dumped out Borussia Monchengladbach from their all-Bundesliga tie.
Follow the draw live below...
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When is the draw?
The draw will take place in Nyon on Friday 17 March, following the completion of the last-16 ties on Thursday.
What time is the draw?
Proceedings will begin at 12.00pm GMT, one hour after the Champions League quarter-final draw.
Where can I watch it?
It will be shown live on BT Sport 2.
Alternatively, you can follow minute-by-minute updates on The Independent's live blog.
How does it work?
The draw is unseeded and there will be no ‘country protection’, meaning teams from the same domestic league can be drawn against each other.
The team drawn first will play the first leg at home, with those drawn second away.
When will the Europa League quarter-finals take place?
The quarter-final first legs will be played on Thursday 13 April, while the second legs take place the following week, on Thursday 20 April.