Five British teams will learn their last-16 opponents when the draws for the Europa League and Europa Conference League take place on Friday.
Liverpool, West Ham, Brighton and Rangers are in the Europa League draw, which takes place from 11:00 GMT.
Aston Villa are in the Europa Conference League draw from 12:00.
All five clubs are seeded, which means they will be away for the first leg on Thursday, 7 March and at home for the second leg on 14 March.
Both last-16 draws, at Uefa's headquarters in Nyon, Switzerland, feature the eight group-stage winners and the eight knockout round play-off winners? of each competition.
The sides that emerge from the eight ties in both cups advance to April's quarter-finals.
No team from the same country can be drawn against each other at this stage.
If the tie is level at the end of the second leg, extra time and penalties will be played - with no away goals rule in place.
Premier League leaders Liverpool lost two of their three away games in Group E, against Toulouse and Union Saint-Gilloise, but still finished top.
West Ham, Europa Conference League winners last season, dropped just three points in Group A while Brighton - who are playing in Europe for the first time - beat Ajax home and away to top Group B.
Scottish Premiership leaders Rangers finished top of Group C after wins over Real Betis (home and away) and Sparta Prague.
Aston Villa made progress in the Europa Conference League after topping Group E with 13 points from six games.
Brighton became the first side to win each of their first two meetings with Ajax in major European competition since Mallorca in 1999, while they are the first English side to do so since Tottenham in 1981
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.
Azerbaijan's Qarabag will be unseeded, meaning they could meet one of several seeded British teams, including Liverpool, West Ham, Brighton and Rangers
The Europa League final takes place at Dublin's Aviva Stadium on 22 May while the Agia Sophia Stadium, Athens, Greece, is the setting for the Europa Conference League final on 29 May.