Among the clubs Liverpool, West Ham, Brighton and Rangers could face in the Europa League are AC Milan, Roma and Sporting Lisbon.
AC Milan, who finished third in their Champions League group this season, lost 3-2 to Rennes in France on Thursday but advanced from the knockout round play-off tie 5-3 on aggregate.
They are third in Serie A and their squad includes former Chelsea players Ruben Loftus-Cheek, Fikayo Tomori, Olivier Giroud and Christian Pulisic.
Sporting Lisbon are level on points with leaders Benfica in the Portuguese League. Their squad includes Enfield-born former Tottenham forward Marcus Edwards.
Marseille, who have former Arsenal and Chelsea forward Pierre-Emerick Aubameyang playing for them, are also in the hat along with Roma, who went through on penalties against Feyenoord on Thursday despite Romelu Lukaku seeing his kick saved.
Ajax and Olympiakos are among the unseeded clubs Aston Villa could face in the Europa Conference League.
Seeded teams for Europa League draw: West Ham, Brighton, Rangers, Liverpool, Atalanta, Bayer Leverkusen, Villarreal, Slavia Prague.
Unseeded teams for Europa League draw: Roma, Marseille, Sparta Prague, Sporting Lisbon, AC Milan, Qarabag, Benfica, Freiburg.
Seeded teams for Europa Conference League draw: Aston Villa, Lille, Maccabi Tel Aviv, Viktoria Plzen, Club Bruges, Fiorentina, PAOK, Fenerbahce.
Unseeded teams for Europa Conference League draw: Sturm Graz, Servette, Union Saint-Gilloise, Dinamo Zagreb, Olympiakos, Ajax, Molde, Maccabi Haifa.
Who will be heading to Azerbaijan?
West Ham, Brighton, Rangers or Liverpool could face a long trip to Azerbaijan in the Europa League on 7 March.
Qarabag reached the last 16 after defeating Portuguese side Sporting Braga 6-5 on aggregate in the knockout round play-offs.
Liverpool face Manchester City in a top-of-the-table Premier League game on 10 March, and Jurgen Klopp will not relish a flight of up to six hours each way before a match of huge domestic significance.
On the same day that Liverpool host Manchester City, West Ham are at home to Burnley and Brighton entertain Nottingham Forest.