The France international, who has long been linked with a move to Spanish giants Real Madrid, is available on a free transfer this summer.
Liverpool, Chelsea and Manchester United have also all held a long-standing interest in Mbappe, but it is thought a move to the Bernabeu has always been his only chosen destination.
Saudi Arabian team Al Hilal made a shock record €300 million bid for the pacey forward in July last year but the move was rejected by the player himself.
It brings to an end a seven-year stint with PSG, where the World Cup winner has won five league titles - including a domestic quadruple in 2019/20.
Most recently, Mbappe netted in PSG's Champions League last 16 first-leg win over Real Sociedad on Wednesday night.
The nature of Mbappe's exit is to be finalised in the coming weeks and months, with the forward earning a reported €200 million per year.
