Celtic were the only former European champions among the 39 teams who featured in the draw for the first and second qualifying rounds of the contest, which will end in Kiev on May 26.
The Scottish side will enter in the second qualifying round where they will face either Linfield, from Northern Ireland, or San Marino champions La Fiorita, who were drawn together in one of the five first-round ties.
Trepca will make the long trip to the Faroe Islands after being paired with Vikingur in the first round tie, with the winners meeting Icelandic champions Hafnarfjordur in the second round.
Kosovo was granted UEFA membership in May 2016 but Feronikeli, the champions at the time, were not granted a UEFA licence for last season's European competitions.
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Serbian champions Partizan Belgrade were paired with Buducnost Podgorica from neighbouring Montenegro in one of the top second round ties. Swedish champions Malmo, who reached the final of the old European Cup in 1979, face Macedonia's Vardar Skopje.
Austrian champions Salzburg, who have made nine unsuccessful attempts to qualify for the lucrative group stage since energy drinks manufacturer Red Bull became sponsors of the club in 2005, will start their latest campaign against either Hibernians of Malta or Tallinn of Estonia in the second round.
There are four qualifying rounds before the group stage where the biggest clubs from Spain, Germany, England and Italy enter the fray.
(Writing by Brian Homewood; Editing by Alison Williams)
