
Liverpool visit French side Toulouse in first-leg action on Wednesday, with Sevilla set to host AEK Athens later that day.
Also on Wednesday, the 2006 finalists Arsenal are at Sparta Prague and 1986 champions Steaua Bucharest visit Belarussian side Bate Borisov.
Five of the 16 ties are on Tuesday, with 1991 champions Red Star Belgrade at Glasgow Rangers with new coach Milorad Kosanovic after the sacking of Bosko Djurovski. The same day, Benfica host Copenhagen and Valencia are up against Sweden's Elfsborg.
The winners qualify for the lucrative group stage for which 16 teams led by title holders AC Milan are directly entered.
Milan beat Liverpool 2-1 for the 2007 title in May. Liverpool coach Rafa Benitez vowed his team will make another attempt this time around and at the same time fight for the Premier League crown as well.
"I am not over that Milan game yet, especially because I know we were so close to winning," he said. "Every year the squad is better and we can manage with both competitions."
The Reds have bolstered their squad with forward Fernando Torres and Dutchman Ryan Babel and gained further confidence ahead of the Toulouse trip by winning the Premier League opener 2-1 at Aston Villa.
Champions League newcomers Toulouse also showed fine form when they beat national champions Lyon 1-0, but coach Elie Baup readily admitted the Liverpool tie will be a learning experience.
"It's the best draw we could have had. This will put us in the spotlight and will allow us to grow. Toulouse don't have a significant place in French football but a match like this will turn all the attention on our club. This will allow us to progress," he said.
The underdog role even more applies to Elfsborg, who surprisingly made it through from the first qualifying round to earn a date with two-time finalists Valencia.
"We go into the tie against Valencia as clear underdogs, but at the same time they have an enormous pressure to succeed," said coach Magnus Haglund.
"Their whole organisation is built up around the Champions League and failure to reach the group stage would be a catastrophe for them. The pressure Valencia are feeling is our chance. If we can play well and keep them at bay at Mestalla anything can happen."
Sweden have not had a team in the group since 2000 (Helsingborg).
Another surprise team from northern Europe are Finland's Tampere, who play Norway's Rosenborg Trondheim.
The only Italian club in the qualifying round, Lazio, meet Dinamo Bucharest on Tuesday. German representatives Werder Bremen take on Dinamo Zagreb on Wednesday.
DPA