Mbappe was decisive in France's triumphant World Cup campaign this summer.
And Bakayoko said of his former AS Monaco teammate: "I'm not surprised about his success.
"He is very young, but he is very mature. He is a very intelligent player and I think that with his characteristics, he is the best player in the world.
"Do not forget he's very young and it's not easy to play against older players and be so fast on the pitch."