The Premier League side had expressed an interest in signing the 23-year-old, and reportedly had €5million bid for the versatile midfielder rejected earlier this summer.
Anita has already said he would be open to moving to the Sports Direct Arena, and recent reports suggested the player has handed in a transfer request to his club to try to force a move to Alan Pardew’s side.
However, Overmars insists Newcastle have not been in touch with him regarding the Netherlands international and has urged the player to remain with the Eredivisie champions.
"If Frank [de Boer] wants to keep him, Vurnon should just stay at Ajax," the former Barcelona and Arsenal star told Voetbal International.
"His contract has two more years left on it and we are very pleased with him. In the two weeks I have been in this role with Ajax I have heard nothing from Newcastle."
Anita, who made 33 Eredivisie appearances last season, scoring two goals, has two years remaining on his contract at the Amsterdam ArenA.