He probably won't get there but he has as much of a chance as anybody will ever have. As you note, his international accomplishments are already insane and he will very likely end up the highest ever World Cup scorer and possibly end up on the very short list of players to win multiple World Cups and the even shorter list who played in three finals.I'm not a soccer fan except for when I watch the World Cup, so I don't know enough about the leagues, etc.
But does Mbappe have a chance at this title in the future? I thought I saw a stat that he is only 1 goal behind Messi in World Cup play (13-12) and only 4 back of the all time record of 16. And he just turned 24, like yesterday. He was certainly the best player I noticed throughout the tournament, but again, I'm a complete novice.
But club soccer is the highest level of competition in the world from a quality of play standpoint and he has a lot of catching up to do there. He has been fantastic at club level too but he hasn't yet played in one of the very best leagues, he hasn't won the Champions League, and he also hasn't won the biggest individual award (the Balon d'Or), which takes into account both international and club performances. Messi was a dominant player on one of the best clubs in the world for nearly 15 years, won three Champions Leagues, and 7 Balon d'Or. Mbappe might not need to match that but he'd have to at least come close - like multiple CL titles and 4-5 Balon d'Or awards - for it to even be a debate.
The 2023 Balon d'Or will take into account this past World Cup and will almost certainly come down to Mbappe v Messi, with their club performances decisive. Which is all the more crazy because they are teammates.