Mbappe entered this summer's competition off the back of scoring 21 times for Paris Saint-Germain last term.
The 19-year-old had been in fine form for France on their run to the final of this year's World Cup, before getting his name on the scoresheet as Les Bleus landed the crown with a 4-2 win over Croatia on Sunday afternoon.
"Kylian Mbappe is the guy that Cristiano Ronaldo and Messi are handing the crown over to. He is the guy who will be standing up on that Ballon d'Or podium in years to come. Easy," Ferdinand told BBC Sport.
"I hope my old club are chasing him! He has that connection with Paul Pogba too."
Mbappe was technically on loan at PSG from Monaco last season, but completed a permanent move to the Ligue 1 giants earlier this summer for a fee that could eventually rise to £159m.