It is not the first time the North London rivals have gone head to head for the signature of an Ajax defender, as they both battled for Thomas Vermaelen and Jan Vertonghen with each club winning one transfer battle for the defenders.
Veltman would add quality and depth to either defence, with both sides are looking for defensive reinforcements this summer.
Vermaelen looks set to leave Arsenal and The Gunners will need to bring in a younger defender who can learn from Laurent Koscielny and Per Mertesacker.
Tottenham were far from convincing in defence last season and Pochettino will look to Veltman to improve his side, with Michael Dawson looking likely to leave and Younes Kaboul a consistent fitness concern for the club.
The young centre-back played 25 times for Ajax last term, and scored twice with two assists to help the side win the Eredivisie title.
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He is currently in Brazil with Louis Van Gaal's Netherlands squad and any move will have to wait until he returns from the World Cup.
Veltman would be reunited with former teammate Vertonghen with a switch to White Hart Lane, though Arsenal can offer him Champions League football.