A fee of around £6.7million is reported to have been agreed between the two clubs and the Magpies now look well-placed to tie up a deal for Anita in time for their opening Premier League game of the season at home to Tottenham on Saturday.
The 23-year-old has won three senior caps for Holland having played for them at various youth levels, but was not part of their squad for Euro 2012.
Able to play in midfield or defence, he came through the academy set-up at Dutch giants Ajax and made his first-team debut in the 2005/06 season.
Newcastle have already signed Romain Amalfitano, Curtis Good and Gael Bigirimana this summer.