Monaco are desperate to keep hold of Mbappe and have already rejected offers from Arsenal and Real Madrid for their star player.
The France international has been linked with a move away from the Ligue 1 champions but has not handed in a transfer request.
Monaco have already sold a host of top stars following their title-winning campaign last season.
And Mbappe looks set to be the next to leave.
That is according to Spanish newspaper Mundo Deportivo, who claim a deal for the 18-year-old could be confirmed ‘within hours’.
Mbappe didn’t feature in Monaco’s 1-0 win Metz last night.
The deal will cost PSG a staggering £183million (€200m), which includes bonuses.
PSG are said to be ready to pay £165m up front for the winger.
The supposed agreement comes after PSG paid £200m to Barcelona for their star player Neymar.
Manager Unai Emery has been given a blank cheque to sign whoever he wants this summer with a remit of winning the Champions League.
Mundo Deportivo claim Monaco boss Leonardo Jardim sent Mbappe home from training yesterday and left him out of the game against Metz.
