Atletico Madrid's Metropolitano stadium will host the final on June 1.
City have been drawn in a group with Shakhtar Donetsk, Lyon and Hoffenheim.
Group B: Barcelona, Tottenham, PSV Eindhoven, Inter Milan.
Juventus are clear favourites in the group where Jose Mourinho's troubled United are likely to battle Valencia for second spot, with debutants Young Boys Bern the rank outsiders.
PSG are one of the most exciting teams in the world and I think their target is to win the Champions League, so that will be two interesting matches.
Teams from the same country could not be drawn together on Thursday, and teams from Ukraine and Russian Federation were also kept apart due to ongoing political tensions. I expected a hard group, we have a hard group and that's what the Champions League is all about. Red Star won the old European Cup in 1991, one year before the format changed.
Group C: Paris Saint-Germain, Napoli, Liverpool, Red Star Belgrade.
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The Spanish giants Barcelona will be expected to top this group as favorites, despite it being the "group of death".
Group E also has three former European champions - Bayern Munich, Benfica and Ajax Amsterdam - alongside AEK Athens. But Dortmund have the Champions League experience although they have a new team with some new players.
Meanwhile, Liverpool are looking forward to facing off against Paris St Germain and Napoli in the group stage of the Champions League, with manager Juergen Klopp anticipating a tough run in the tournament.
But Allegri also said that the choice of Modric must be respected.
"It could have been worse, but we cannot afford negligence if we want to finish first", said Bayern forward Thomas Mueller. All 32 teams get a basic €15.25 million (US$17.8 million) just for being in the draw. After meeting with the Germans, the locals will have to stay in Lyon, then the miners have two games with Manchester city, to be followed by a trip to Hoffenheim.
Lokomotiv Moscow, seeded in the top pot as Russia's champion, will play Porto, Schalke and Galatasaray in Group D.
The group is completed by Valencia and Swiss club Young Boys.