Having conquered Europe as Porto coach in 2004 and last season with Inter Milan, the Portuguese has taken his special qualities to the Bernabeu having replaced Manuel Pellegrini.
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"Real Madrid want their 10th (European Cup) just as much as I want my third but we both know it's very difficult," Mourinho told a news conference on Tuesday.
Real, who have not gone beyond the last 16 for the past six seasons, have been handed a testing Group G to negotiate with AC Milan and Auxerre, the other two sides, meeting in the San Siro.
Last season's runners-up Bayern Munich begin in Group E against AS Roma while English double winners Chelsea travel to Slovakia to play new boys MSK Zilina in Group F.
Chelsea manager Carlo Ancelotti took the unusual step of naming his side 24 hours before kickoff with midfielder Yossi Benayoun making his first start since joining from Liverpool.
Spartak Moscow will seek their 100th European victory when they face Olympique Marseille in the other match in the section.
Arsenal welcome Portuguese side Braga in Group H without several first team players including strikers Theo Walcott and Robin van Persie and Shakhtar Donetsk host Partizan Belgrade.
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