Arsenal saw a bid for the youngster rejected last season but Wenger has publicly courted Mbappe over recent months, hailing him as a potential successor to Thierry Henry.
And the Arsenal manager revealed in an interview with beIN Sports that he had made a personal plea to convince Mbappe to make a switch to the Emirates before he signed a new contract in March 2016.
“The player would tell you that I was at his home last year to try to get him here,” Wenger said. “Because he was at the end of [his] contract but Monaco managed to keep him and the decision was very, very tight.
“But I could understand it as well because he was educated there and at the end decided to stay there.”
Speaking last month Wenger had offered a downbeat assessment of Arsenal’s chances of acquiring Mbappe, hinting he had already been priced out of the race for the 18-year-old, who has emerged as one of Europe’s most coveted players after a breakout season at Monaco.
His comments diverged sharply from former Arsenal star Robert Pires, who said he was convinced Wenger could convince Mbappe to move to the Emirates.
Monaco remain insistent that they will not part with their brightest young prospect, who has scored 24 goals this season, at least for the time being.
Wenger conceded that it may be best for the 18-year-old to remain in Ligue 1 next season but suggested that if Mbappe were keen on a move to the Emirates he would certainly be welcome.
“Can Arsenal get him? I don't know, that's down to him. You know certainly as I do that today he will decide where he goes and say: Real Madrid? Maybe. Barcelona? Maybe. Arsenal? Manchester? He can go where he wants.
“So I don't know what is his deep aspirations but maybe the best thing for him is to stay one more year at Monaco.”