Mbappe won the FIFA Young Player award for his performances at Russia 2018 after helping France claim the FIFA World Cup on Monday (AEST).
The 19-year-old forward scored in France's 4-2 victory over Croatia in Moscow as he took his tournament tally to four goals.
Mbappe – who completed a permanent transfer to Ligue 1 champion PSG from French rival Monaco during the off-season having spent last term on loan in Paris – has no plans to leave the capital as Madrid attempt to replace Juventus-bound Cristiano Ronaldo.
"I will stay with PSG, continuing on my path with them," Mbappe said.
"I am at the beginning of my career."
Mbappe enjoyed a stellar 2017-2018 campaign with PSG, scoring 21 goals in all competitions.