The 22 year-old has enjoyed a breakout season at the Dutch side with the likes of Vertonghan and Alderweireld leaving which has led to his promotion into the starting line-up.
This form has even led to him receiving a cap for the national team under the likely new Manchester United coach Louis Van Gaal.
Van Gaal is reportedly keen to have the youngster playing under him at his next club while Arsenal are said to be interested in the defender who would come in to challenge Koscielny and Mertesacker for their starting postions.
"Word is that Arsene is quite keen on Veltman at Ajax", an Arsenal insider revealed. "If Vermaelen goes, we'll need another option there. The problem is, Van Gaal is a fan of his and might try signing him, depending on where he goes this summer."