The 23-year-old has established himself as a key member of the Ajax side and helped Frank De Boer's side win the Dutch title this season.
Magpies boss Alan Pardew is believed to have watched Anita in action on several occasions and the player's representative, Harry Lulofs, claims Newcastle have tabled an offer to Ajax for the defensive midfielder.
Lulofs also revealed former Norwich boss Paul Lambert was keen on Anita and has hinted he could move for him now he has switched to Aston Villa.
"Ajax are very satisfied with the guy [Anita] and want to keep him, but Newcastle have been watching him for a long time and really want to sign him," Lulofs is quoted as saying in The People.
"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."