Everton will face either Ruzomberok of Slovakia or Norwegian side Brann in their Europa League third qualifying round tie.
The Toffees finished seventh last season in the Premier League and were England’s top seeds in Friday’s draw in Nyon, with Manchester United having secured a place in the Champions League after winning the Europa League final against Ajax last season.
Bran currently hold a slender 1-0 lead from the first leg of their second qualifying round tie, which was played on Thursday night in Slovakia. The second leg will be on July 20.
Scottish Premiership side Aberdeen will meet either Apollon Limassol of Cyprus or Moldovan outfit Zaria Balti, if they can get past NK Siroki Brijeg.
The Bosnian’s secured a 1-1 draw in the first leg of the second-qualifying round tie with the Dons at Pittodrie on Thursday.
League of Ireland Premier Division sides Cork City and Shamrock Rovers also have work to do if they are to progress into the third qualifying round.
Cork lost 1-0 at home against Cypriots AEK Larnaca on Thursday night, while Shamrock Rovers were beaten 3-2 at home by Czech side Mlada Boleslav.
Should Cork reach the third qualifying round, they have been paired with Rabotnicki of Macedonia or Belarus team Dinamo Minsk. The first leg of that tie ended 1-1 in Skopje.
Shamrock Rovers were drawn against either Kazakhstan side Kairat Almaty or Albanians Skenderbeu, who are also locked at 1-1 ahead of the return leg in Korce.
Friday’s draw saw 29 fixtures decided, which were split into five groups, with the first legs set to be played on July 27 and the second on August 3.
Italian club AC Milan will face CSU Craiova of Romania, while Ligue 1 side Marseille tackle Oostende of Belgium.
Dutch team PSV Eindhoven will take on the winner of Croatian outfit Osijek or Swiss club Luzern while Turkish giants Fenerbahce meet Austrians Sturm Graz or Mladost Podgorica of Montenegro.
The winners will then advance to the Europa League play-off round, which will also include the 15 losers from the Champions League third qualifying round.
The draw for the Europa League group stages will be made on August 25, with 16 teams having gained automatic entry – including FA Cup winners Arsenal, who finished fifth in the Premier League to miss out on the Champions League for the first time in 20 years.