A host of elite clubs have been keeping tabs on Mbappe’s situation following his breakthrough season in Ligue 1.
The teenage striker netted 26 goals last season to help Monaco beat Paris Saint-Germain to the title while also reaching the semi-finals of the Champions League.
Wenger is understood to be a huge admirer of Mbappe but is now resigned to missing out on the 18-year-old as Real Madrid step up their interest.
According to the Daily Telegraph, Wenger is now intent on pursuing Monaco and France midfielder Lemar, who has already been the subject of two rejected bids from the Gunners.
Monaco are reluctant to lose any more star players ahead of the 2017-18 campaign but Wenger is said to have made Lemar one of his top targets.
His arrival at the Emirates could pave the way for Alexis Sanchez’s departure, after the Chilean admitted he hoped to be playing Champions League football.
Thomas Lemar 2016/17 stats
Premier League champions Chelsea and Manchester City have expressed interest in Sanchez but Arsenal will need to be persuaded to sell to a direct rival.
Speaking about his future to Radio Sport, Sanchez said over the weekend: ‘The truth is that the decision doesn’t depend on me. I have made my decision, but now we wait for a response from Arsenal.
‘It depends on them, I have to wait to know what they want. My idea is to play and win the Champions League, it is a dream I have had since I was little.’