Arsenal will face Serie A outfit Udinese, a draw which looks tough on paper but may not be so tricky in reality against a club who have sold their two most important players and will not have played a competitive match beforehand.
Four-times European champions Bayern and Arsenal were spared the long trip to Russia to face Rubin Kazan, a task which fell to France's Olympique Lyon.
Former European champions Benfica must play Twente Enschede and Spain's Villarreal were pitted against Odense of Denmark in the so-called "league" side of the draw, featuring non-champions from Europe's strongest domestic championships.
"That is an achievable and interesting task," Bayern coach Jupp Heynckes told the Bavarian club's website. We have an excellent chance to qualify for the group stage. Avoiding Rubin meant we will not have any complicated travelling to do."
Failing to qualify for the group stage would be unthinkable for Germany's biggest club, especially in a year when they are hosting the final.
"It's a very difficult match against one of the most important clubs in Europe," said Collavini, whose club have sold winger Alexis Sanchez to Barcelona and midfielder Gokhan Inler to Napoli.
"We are working to complete our squad for the end of August. It's important to have the opportunity to play a club like Arsenal."
Of the sides to won their domestic championships FC Copenhagen, who last year reached the last 16, were drawn against Viktoria Plzen from the Czech Republic while former European Cup runners-up Malmo will play Croatia's Dinamo Zagreb, who last qualified in 1999/00.
Five places are reserved for the champions from lower-ranked nations in the group stage.
