Newcastle have already seen one bid in the region of £5million rejected as Ajax are reluctant to lose the 23-year-old, and are thought to be holding out for a fee of £8million for the midfielder.
Anita is keen to make the move to the Premier League and is hoping Newcastle can strike a deal with Ajax.
Anita is understood to have held talks with Ajax's new sporting director Marc Overmars on Tuesday and has told the club that he wants to move on.