Newcastle have immediately sent out feelers for potential managerial candidates after announcing Rafa Benitez is leaving the club.
TMW says Gattuso is on their shortlist, though is yet to hear from Toon reps.
While in charge of Milan, Gattuso was linked with Newcastle.
In April, it was suggested he'd discussed applying for the Newcastle job during a meeting with agent Jorge Mendes.
“I see Mendes often, I like good food and to talk about football," Gattuso later explained.
“The rumours about Newcastle are unfounded.
"I repeat, I only have a great friendship with Mendes."