The Frenchman wanted to bring the speedy winger to the Emirates Stadium back when he was at Monaco.
However, he was playing regular football and eventually secured a move to Paris Saint-Germain instead.
"It was a footballing blow, and an obvious one too. Seeing a photo (of Mbappe wearing an Arsenal shirt), hurts my heart a little," Wenger told French broadcaster TF1.
"I went to his parents and tried to convince them. At the time, he was a little shy, people were starting to ask him for his first autographs in Monaco.
"At the beginning of your career, you don't have too much pressure at the start and they managed to persuade him to extend it by promising him that he would play more easily at Monaco than at Arsenal, Liverpool or Real Madrid.
“We can say that his parents advised him well and that he made the right decision."