The 20-year-old suggested he is considering his Paris Saint-Germain future and admits he is open to a “new project”.
Former Monaco forward picked up both the Player of the Year and Young Player of the Year awards.
But after accepting his prize from Didier Drogba, the forward said: “It’s a very important moment for me, I’ve come to a turning point in my career.
“I have discovered a lot here, and I feel it is perhaps the moment to have more responsibility.
“I hope that can maybe be at Paris Saint-Germain, that would be a great pleasure. Or perhaps elsewhere with a new project.”
Mbappe scored 32 goals as PSG retained the League 1 title, but the club once again failed to deliver the Champions League ambitions of their billionaire Qatar owners.
PSG let a two-goal first-leg advantage slip against Manchester United and was eliminated at the last-16 stage.
Mbappe stood by his comments after the ceremony, adding: “I said what I had to say.
“When you are in such an occasion you can send messages, I think I have sent mine.
“If I speak more it will be too much and that is not the message I wish to send.”
Earlier this year, Real Madrid’s president suggested Zinedine Zidane could use his French connection to lure Mbappe to the club this summer.
“Zidane is French, so with Mbappe he could do something,” said Florentino Perez.
Pep Guardiola dismissed reports Manchester City could sign Mbappe in October last year.
“Manchester City don’t have and are not going to spend, the money that maybe Mbappe deserves, or PSG deserves,” he said.