Celtic are set for a rematch with Rosenborg if they get past Armenian side Alashkert in their opening Champions League qualifier.
Brendan Rodgers’ side will face the winners of the tie between Icelandic champions Valur and first-round seeds Rosenborg if they reach the second qualifying round.
Celtic are scheduled to open their quest for a hat-trick of group stage qualifications in Armenian capital Yerevan on July 10-11, one round earlier than last season, but final dates are still to be confirmed.
Alashkert knocked St Johnstone out of the Europa League three years ago after they scored a crucial away goal with 10 men at McDiarmid Park, but their only other European victories have come against Santa Coloma of Andorra.
A James Forrest strike in Trondheim proved enough to ease Celtic past Rosenborg last year at the third qualifying-round stage. The Norwegians dropped into the Europa League qualifiers, where they beat Ajax to qualify for the group stages.
Valur have only won three European ties despite qualifying 22 times. They beat Ventspils of Lativa 1-0 last season in the Europa League before losing 5-3 on aggregate to Slovenians Domzale in the second round.
Celtic beat them 7-0 at Parkhead in the European Cup Winners’ Cup in 1975-76 but those sorts of defeats are not confined to the distant past for the Reykjavik side – they lost 10-1 over two legs to Danes Brondby two years ago.
Northern Irish champions Crusaders were paired with Ludogorets, the highest-ranked team in the first round.
The Bulgarians have twice reached the group stages in the past four seasons, playing Liverpool and Arsenal along the way.
Crusaders will face Dudelange of Luxembourg or Hungarians Videoton if they pull off a shock.
The New Saints, who were seeded in the first round, will face Macedonian champions Shkendija, who lost on away goals to Aberdeen in the Europa League three years ago. A tie against Moldovans Sheriff or Georgian team Torpedo Kutaisi awaits the winners.
Cork City were handed a tough encounter against Polish side Legia Warsaw, although they were given a boost when the losers of their tie were earmarked as automatic entrants to the third qualifying round of the Europa League.
The rest of the first-round losers will enter the second round of the Europa League qualifiers in a new champions path.
Crusaders will play Olimpija Ljubljana or Qarabag if they drop down, while TNS will play the beaten finalist of the four-team preliminary round.
Celtic would likely face Sutjeska of Montenegro if they suffered a shock defeat against Alashkert. Sutjeska face Astana of Kazakhstan in the Champions League qualifiers.