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There has been widespread media speculation that Mbappe will move to Real Madrid. Mbappe did not mention the Spanish champions in his video but confirmed he would leave France.
Hummels headed home from a corner five minutes into the second half to send the Germans, who won the title in 1997, into their first final in Europe's top club competition since 2013.
PSG, fresh from being crowned Ligue 1 champions and desperate to win their first ever Champions League trophy, found it hard going against a disciplined German defence, especially in the first half with forward Kylian Mbappe largely neutralised.
PSG will face Borussia Dortmund in the semifinals after the Germans beat Atletico Madrid.
PSG came into the match unbeaten in their last 27 games in all competitions but were undone by a fired-up Barcelona side looking to return the club to the summit of European football.
Zaire-Emery became the youngest ever French goalscorer in the Champions League at 17 years and 280 days.
City started their title defence by coming from behind to beat Red Star Belgrade 3-1 at home.
There was no immediate comment from the Ligue 1 champions, owned by Qatar Sports Investments, but French newspaper L'Equipe said the deal could net 31-year-old Neymar 160 million euros ($175 million).
PSG opened their Ligue 1 title defence with a goalless draw at home against Lorient on Saturday as the team's prize asset watched from the stands.
The practices have allowed PSG, owned by Qatar Sports Investments since 2011, to sign top players and coaches 'well above its potential in a normal market situation', LaLiga alleges in the complaint filed on Saturday.