But according to the man himself, the north London club may be out of the running after he outlined what he wants to achieve in the game.
The 18-year-old wonderkid burst onto the scene this season after stunning the world on the biggest stage of them all, the Champions League.
He made history in the elite competition by becoming the first player to score in each of his first four knockout games.
Arsenal, who had already been keeping tabs on the forward, are keen to make a move this summer, but have a lot of competition.
Champions League winners Real Madrid are also very keen on the youngster, and, like Arsenal, have been aware of him for some time.
To make matters worse, Los Blancos boss Zinedine Zidane is the teeanger’s idol, and it seems he would favour a move to Madrid over north London.
Speaking to French outlet TF1 in a recent interview, Mbappe opened up about his own ambitions in the game and outlined exactly what he would like to achieve.
“The Champions League is a dream, a competition that everyone wants to win and that only a minority can win — the most important are the titles,” said Mbappe.
“That would be much more of an obsession for me than the Ballon d’Or, for example.
“I want to touch the stars and, when you dream, you do not dream of playing the middle of the table or maintaining it.
“The 2018 World Cup is the number one goal at international level. As I always say, dreams are good but it’s up to me to work for them.”
Obviously Mbappe has many years ahead of him in which to reach the top of his game, but his comments undoubtedly put Arsenal on the back foot in the race for his signature.
The Gunners missed out on Champions League football for the first time under Arsene Wenger, and it seems this could have a profound effect on the club.