The 18-year-old, who only made his first-team breakthrough last season, has been the subject of constant transfer speculation in the off season after a scintillating first season in professional football.
Mbappe scored 26 goals in 44 appearances for Monaco in all competitions last season, earning huge praise and getting comparisons with Thierry Henry.
PSG have already blown the world transfer record out of the water with the Neymar deal last week and look set to splash the cash further with a rumoured £162 million bid for Mbappe, helped by agent Mendes as reported by the Gazzetta dello Sport.
Real Madrid and Manchester City are both keen admirers of the forward and have been linked with bids for him.
Madrid in particular could look to sign the forward, particularly if they decide to let Gareth Bale leave the Bernabeu.