Spurs head coach Roberto De Zerbi has already sealed the signing of former Liverpool star Andrew Robertson and is making it his mission to strengthen the squad before the start of the new campaign.
Tottenham’s next target is Van Hecke, who has one year left on his contract at Brighton and who has worked at the south coast club under the Italian.
The North London side already has a bid rejected for the Dutchman last month and have not let up as they launched a second offer this week.
As per Brighton chief executive Paul Barber, the Seagulls have turned down two offers for the defender who they are said to be valuing at around £70M.
"There's always going to be a lot of interest in our best players, and certainly in the case of Jan Paul.
“We've been very clear that that interest has been ongoing for a while, and it's coming from multiple sources.
"We have rejected a bid from Tottenham over the last week, in fact (it was) two bids. It has to be right for us, as well as the player."
De Zerbi is also reportedly interested in Manchester City's Savinho and Marcos Senesi from Bournemouth in what is looking like a huge summer spend as they build a team worthy of surviving relegation.