France captain Mbappe last week announced that he will leave the French champions at the end of the season after a seven-year stay, during which he became their all-time top scorer with 256 goals.
Mbappe's frustration lies with PSG's performances in the Champions League, a trophy they have never lifted despite huge investment in the squad. He has been heavily linked with a move to Spanish giants Real Madrid, who are in the final this year seeking a 15th European crown.
His compatriot Dembele joined the Parisian club, who have won 10 of the last 12 Ligue 1 titles, from LaLiga side Barcelona in August last year, signing a five-year deal.
"I have shared and played with incredible players, like Dembele who is here, he is a friend and one day he will pick up this award," Mbappe said on Monday at the award ceremony.
"I thank the club as a whole, the coach, who has helped me and trusted me, his staff, the doctors, all the people at the club, the sporting management, the president, the shareholders of the club, of course, the Emir of Qatar who came to find me at the age of 18, who has accompanied me in all my decisions..."
He said his next chapter is going to be very exciting but did not reveal any further details.
"Now I'm turning the page in my life. Everything that comes next is super exciting, but that's another subject," Mbappe said.
"Thank you all, I'm going to miss you. I have always tried to do my best, and I also want to thank my family, who have always been with me in good times and bad.
"My father, who is here, I know that it was very important to him that I made history in Ligue 1 before I left and I think that with humility I have done everything you wanted."
