The 18-year-old is currently one of the most sought-after prospects in world football following his breakout season for the French champions, which saw him register 15 goals in 29 league appearances.
Wenger has been given significant financial backing this summer as he looks to restore Arsenal to the Champions League in 2018-19, and has already shattered the club's transfer record with the £50m+ capture of Alexandre Lacazette from Lyon.
Arsenal are said to have had a bid of £87m for Mbappe already turned down, with Monaco holding out for a mammoth £130m, and Wenger is said to be giving serious thought to breaking the world transfer record in order to land his man.
According to The Express, Wenger had a three-hour meeting with Mbappe on June 14 following France's international friendly with England and is thought to have assured him that he would be given the chance to spearhead the Arsenal attack and emulate his hero Thierry Henry if he chose a move to the Emirates.
Real Madrid have since emerged as the more likely destination for Mbappe this summer, however, following talks between the two parties in the last few weeks.