The Danish international has impressed in German football.
SportBild is reporting in their print edition, as reported by Sport Witness, that Tottenham are interested in the Danish defender – who could be available for a fee in the region of €15 million (£11.7 million) from current club Werder Bremen this summer.
The report also suggests Spurs continue to be interested in former Chelsea player Andre Schurrle of VfL Wolfsburg. Spurs were already linked with Vestergaard by Bild in March but this is the first time a fee has been mentioned.
Werder Bremen are strapped for cash at the moment and Vestergaard is one of their biggest assets. Bundesligs rivals Borussia Monchengladbach also appear to be keen on the player – who has six caps for the Danish national team.
The 23-year-old, who stands a giant 6ft 6ins tall, would be an odd signing for Spurs – who have good options at centre-back already.
Spurs are blessed with some great defenders, with Toby Alderweireld, Jan Vertonghen and Kevin Wimmer all at their disposal - as well as youngster Cameron Carter-Vickers coming through the ranks and Eric Dier also capable of playing the role.