Zoet has spent the last two seasons on loan at Eredivisie rivals RKC Waalwijk and has been watched by Sunderland whilst playing for Holland Under-21s in the European Under-21 Championship in Israel.
Holland qualified from the group stage only to be knocked out by Italy in the semi-finals last week.
The highly rated keeper was also linked with Fulham last summer but PSV were said to have rejected their offer.
Paolo Di Canio's pursuit of Zoet is bound to raise question marks over Simon Mignolet's future at the club.
The Black Cats' current number one is reportedly being chased by Liverpool.