The right-back only moved to Heerenveen last summer from Sparta Rotterdam but is now keen to join the Dutch champions.
PSV have agreed a fee in the region of 6million euros with their Eredivisie rivals and Dumfries will now hold talks over personal terms with the Eindhoven outfit.
The 22-year-old was an ever-present for Heerenveen last season and managed four goals in the Eredivisie.
Dumfries represented the Netherlands at youth level but is now an Aruba international and has two caps so far, with one goal.
Preston are reportedly weighing up whether or not to make a fourth offer for Peterborough United left-back Andrew Hughes.
James Maddison has completed his move from Norwich City to Leicester City for an undisclosed fee.