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.