Manager Arsène Wenger signed a two-year extension to his contract this week and the 18-year-old French striker is said to be high on his wish list this summer.
Stunning breakthrough season
Mbappé's breakthrough this season has taken everyone by surprise, with the teenager playing a key role in Monaco's first Ligue 1 title in 17 years.
However, it was his performances which helped his side reach the semi-finals of the UEFA Champions League which seems to have grabbed the attention of Europe's elite.
The striker became Monaco's youngest-ever first team player when he made his debut in December 2015 but it is this season where he has really made a name for himself.
He scored 17 goals in 29 appearances in Ligue 1 this season as well as managing six goals in nine appearances in the Champions League.
Arsenal face stern competition
Arsenal are not the only club to have already shown their interest in Mbappé this summer. This bid is said to already be the third one which the French outfit has turned down already.
However, despite all of this interest from top clubs across Europe, Monaco still remain determined to keep Mbappé beyond this transfer window.
Having already sold Bernardo Silva to Manchester City for £43 million and rumours that Benjamin Mendy and Tieomoue Bakayoko could also depart, the French outfit will be determined to keep their most prized asset.
Alexis Sánchez on his way out?
Arsenal's interest in Mbappé is undoubtedly going to raise further questions about the future of Alexis Sánchez.
With Arsenal needing to put in a serious challenge to win the Premier League title next year, adding Mbappé to their squad and keeping hold of Sanchez and Mesut Özil would be a good start.
However, if Sánchez was to leave, then the addition of a player such as Mbappé would arguably be a necessity.