The versatile 23-year-old, who can play as a defensive midfielder and as a full-back, has enjoyed back-to-back Eredivisie titles with the Dutch giants.
And now it seems Alan Pardew's men are making their move for the Holland international with three caps to his name.
Anita's representative Harry Lulofs said: "Ajax are very satisfied with him and want to keep him, but Newcastle have been watching him for a long time and really want to sign him.
"This is the first offer Ajax have received for Vurnon and we'll soon see how they react.
"The only other Premier League club to get in touch was Norwich. Paul Lambert called me to ask about him.
"Now he has moved to Aston Villa so maybe they will be in touch. I don't know."