The Magpies are currently on the lookout for new signings, with a potential takeover of the club on the horizon.
Manager Rafa Benitez missed out on several transfer targets during the summer, with reports claiming he could walk away after growing frustrated with the lack of new arrivals.
Elliot is the club's current number one keeper, with Karl Darlow and Freddie Woodman currently pushing him for a first-team spot.
Newcastle have been linked with the likes of Willy Caballero, Pepe Reina and Orestis Karnezis in the last few weeks but Cillessen is now top of their wish list.
The Dutchman has yet to make an impact since leaving Ajax for the Nou Camo and reports now claim the 28-year-old is desperate for more first-team action.