The France striker has scored 36 goals in all competitions this season, netting a hat-trick against former side Monaco on the day PSG were confirmed as Ligue 1 champions, following Lille's draw with Toulouse.
"I am here, I am in the project," said Mbappe of PSG.
"It's good for Real Madrid if there is Zizou, but I will watch merely as an admirer."
With the hat-trick, Mbappe became the first Ligue 1 player since Jean-Pierre Papin in 1989-90 to score 30 league goals.
Since making his debut for Monaco in 2015 aged 16, Mbappe has scored 59 goals in Ligue 1.
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