On Thursday night, Villa produced a dominant performance to see off Ajax - another of the tournament favourites - by a 4-0 scoreline in the second leg of their last-16 tie.
However, based on current form, the Premier League outfit have been handed a tougher test in the last eight with French side Lille their opponents.
Lille sit in fourth position in the Ligue 1 table, while they are yet to lose in this season's Europa Conference League, recording six wins and four draws as well as defeating Sturm Graz in the previous round.
Whoever prevails from the tie between Villa and Lille will square off against either Olympiacos or Fenerbahce in the semi-finals, with Villa or Lille at home in the first leg.
Last season's runners-up Fiorentina have been handed a two-legged tie with Viktoria Plzen, with the Italian side at home in the second leg.
The winners of that contest will go up against either Club Brugge or PAOK in the semi-finals.
All first-leg ties at the quarter-final stage will take place on April 11, with the reverse fixtures being staged a week later.
Quarter-final draw in full:
Club Brugge vs. PAOK
Olympiacos vs. Fenerbahce
Aston Villa vs. Lille
Viktoria Plzen vs. Fiorentina
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