The 20-year-old added Ligue 1 player of the year to his already impressive list of honours on Sunday and took the opportunity to say he wanted "more responsibility" in the future, adding it would be either at PSG or "somewhere else".
The world champion, who has scored 32 goals in Ligue 1 this season, has been sharing the front line at PSG with Uruguay striker Edinson Cavani and Brazil's Neymar.
"It's a turning point, it was the moment to say it," Mbappe was quoted as saying by L'Equipe on Monday.
"I am whole. When I say something, I mean it. I said it. If it is at PSG, that's good, if it is elsewhere, it is elsewhere."
Mbappe, whose influence at the French champions grew when Neymar was sidelined with a foot injury this year, has always said he would love to play at Real Madrid.
Mbappe's departure would be a huge blow for PSG, who were knocked out of the Champions League last 16 by Manchester United in embarrassing fashion this season.
It would, though, allow them to stabilize their finances after they were probed for an alleged breach of the Financial Fair Play rules.
Proceeedings in that case were halted in March when the Court of Arbitration for Sport upheld an appeal over a procedural error from governing body UEFA.
