A repeat of the 2014 Champions League final between Real Madrid and Atletico Madrid is still possible after Friday's semi-final draw.
Real, who won that game 4-1 after extra-time, will play first-time semi-finalists Manchester City, with the first leg in north-west England.
Atletico, who beat holders Barcelona in the last eight, host Bayern Munich in their first leg.
Bayern manager Pep Guardiola misses what would have been a difficult semi-final for him personally against City, the Premier League side he will take charge of next season.
"It's a great tie against the team that has won the competition the most times," Txiki Begiristain, Manchester City's sporting director, told reporters.
"But we have got this far and we want to keep dreaming.
"I think that Madrid are the favourites. They have been in the semi-finals 27 times, six in a row. But Paris (St Germain)were also a great team and we were able to knock them out."
Real, record 10-times champions, are unbeaten in their last eight games against English clubs. Their only previous tie against City came in 2012 when the Spanish side won 3-2 at home before drawing 1-1 in Manchester.
For Cristiano Ronaldo, who scored a hat-trick to win the quarter-final against Vfl Wolfsburg, it will be another return to Manchester, where he spent six years with United before moving to Spain in 2009.
The Madrid manager at that time was Manuel Pellegrini, now in charge at City until Guardiola replaces him. The Chilean was sacked by Real after only one season.
Emilio Butragueno, Real's head of public relations, said that in Sergio Aguero, David Silva and Kevin de Bruyne, City had players to win a game on their own.
"It's their first semi-final and they are anxious to do something big in Europe," he added.
"We'll have to be at our best in the two games. Last year also people said we were lucky when we got Juventus and we were knocked out. The two games are going to be very tight."
The only time Atletico have met Bayern was in the 1974 final, when the German side won 4-0 in a replay after a 1-1 draw.
"A team that eliminates the title holders has to be taken very, very seriously," said Bayern board member Andreas Jung.
"We face a tough rival," said the German club's midfielder Javi Martinez.
Jose Luis Caminero, Atletico's sporting director and former player, described the tie as "complicated" but promised the Spanish side would "compete to our maximum as we always do".
City will host Real on April 26 and Atletico face Bayern the following evening.
The final is in Milan on May 28.
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