The focus is, among other things, on identifying individuals who support the USA's ambitions to gain control over Greenland, the newspaper writes.
According to sources, a classified message has been sent to several heads of authorities, including the head of the intelligence service CIA and the head of the national security agency (NSA).
The USA's intelligence chief Tulsi Gabbard, says in a written statement that "The Wall Street Journal should be ashamed of helping actors within 'the deep state', who are trying to undermine him by politicizing and leaking confidential information".
Denmark's Foreign Minister Lars Løkke Rasmussen is concerned and says on his way to the EU's Foreign Ministers' meeting in Warsaw that the USA's ambassador in Copenhagen is being called in for an explanation.
One does not spy on friends, Løkke emphasizes.
The USA's President Donald Trump has repeatedly expressed that he wants to take over Greenland and has said that he does not rule out a military operation to gain control over the island.
Greenland and Denmark have, in turn, rejected all American proposals.