Le Parisien says contact has been maintained between the two parties in recent days as PSG explore the prospect of bringing the midfielder back home.
Bakayoko, while a former AS Monaco player, was born and raised in the suburbs of Paris.
PSG chief Leonardo rates the France international highly and would welcome taking Bakayoko on-loan this season.
AC Milan also remain in contact with the player's camp ahead of next week's transfer deadline.
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