The midfielder, reports TMW, is the subject of an approach from China's Beijing Guoan.
Beijing Guoan are willing to pay Kessie a €10m salary to tempt him to the Far East.
Kessie is on a two-year loan at Milan from Cesena and a permanent deal will not be assessed until the end of this season.
The frustration for the midfielder is that Milan are reluctant to upgrade his contract, whereas a move to China would net him €50m.
PSG are also monitoring developments.