Mbappe has established himself as one of the brightest prospects in world football over the past two years and has increased his reputation even further by scoring three goals to help France to the final of this summer's World Cup.
"He's a kid that I know. I've seen him play the last few years and I know the people who helped him to be the player he is now," Drogba is quoted as saying by Sky Sports News.
"I'm very happy for him. And if he continues like this, why not? Why not win the Ballon d'Or? I had the chance to meet him and we had an important meeting with a lot of influential people in France, with the president Mr Macron.
"We were exchanging ideas and when he started speaking I can tell you that the kid is 19-years-old but he's not a kid. He's very mature and he's very composed when he's talking."
Mbappe is the highest-scoring teenager at a World Cup since Pele scored six goals at the 1958 edition.