The experienced Frenchman was heavily linked with a move to Parc des Princes after announcing the end of his iconic 22-year tenure in north London.
PSG eventually opted to hand their reins to ex-Borussia Dortmund coach Thomas Tuchel, but Wenger continues to see a possible directorial role in the French capital talked up.
Such a position would at least give Mbappe the opportunity to sound out the 68-year-old on ways that he could improve his game, with the 19-year-old a big fan of the three-time Premier League title winner.
Asked by C8TV to name any manager he would like to play under in the future, the France international said: “I dream of being managed by Arsene Wenger.
“He is French, he's had a great career and now he is free because he has left Arsenal.”
While hoping that he will get the chance to work with Wenger at some stage, Mbappe has already shunned one opportunity to make that dream a reality.
Having become one of the most sought-after talents in world football on the back of a Ligue 1 title-winning campaign at Monaco in 2016-17, the exciting youngster had several options to consider.
He eventually decided to link up with PSG on an initial loan agreement which will become a €180 million (£166m/$214m) transfer this summer, but only after turning down the chance to join Arsenal.
Mbappe told reporters in September 2017: "Yes, I met with Arsene Wenger, who is a great coach. He has a great reputation here in France, he's well-respected and knows how to develop young players.
"This was a real option for me. But, of course, Paris Saint-Germain was the main option. We weighed up the advantages and disadvantages of all the clubs but my family told me it had to be my decision and one I needed to make.
"It also had to be a long-term decision. So it was up to me and I decided to come here in order to develop."
Mbappe netted 21 times for PSG across all competitions in his debut campaign and is now chasing down World Cup glory with France at Russia 2018.