After scoring 23 goals in 41 appearances this season, the 18-year-old attacker has been heavily linked with a transfer to Real Madrid but the Gunners remain intent on trying to pull off what could potentially be the signing of the summer.
It has previously been suggested that they had failed with an offer of £87m but according to L'Equipe, Wenger is prepared to go significantly higher in order to take the teenager to the Emirates Stadium.
Wenger has publicly spoken of his admiration for Mbappe, but the French international is known to be keen to work with Real Madrid coach Zinedine Zidane at some stage in his career.
It has previously been claimed that Zidane could prove to be the deciding factor, but it appears that Arsenal and Wenger refuse to bow out of what is becoming a two-way battle.
Mbappe has indicated that he is not against the idea of remaining at the Ligue 1 champions for at least another 12 months.