Spurs are keen to sign the Dutch centre-back this summer, having already wrapped up a Bosman signing of Marcos Senesi from Bournemouth, amid uncertainty over the future of captain Cristian Romero.
Van Hecke is expected to leave Brighton this summer with just one year left to run on his contract, and Brighton chief executive Paul Barber has confirmed that Spurs are not the only interested team. Liverpool and Newcastle have also been linked.
Brighton are reportedly demanding £70million to sell the 25-year-old, with Spurs having first bid around £40m. Another offer from Spurs has now been rejected, with another expected.
Barber told talkSPORT: "There's always going to be a lot of interest in our best players, and certainly in the case of Jan Paul.
"Yes, we have rejected a bid from Tottenham over the last week or so, in fact, two bids. From that point of view, it has to be right for us as well as the player.”
He added: "We have to be in a position to make the best trades to suit our model and also to make sure that we're supporting Fabian [Hurzeler, Brighton manager], because he's got another big season ahead of him.
"He's had two seasons in the Premier League, he's finished eighth on both occasions, this time we've been fortunate enough to qualify for a European competition.
"We want to go as deep in that competition as we can, while also doing well in the Premier League.
"To do that, we need to make sure Fabian's got the best possible squad and we've got the right balance between the young players that typically we like to bring in and develop, and the more experienced players like Pascal Gross and others, who can actually help us progress in all of the competitions that we're in.
"As always, it's a balancing act, and hopefully this summer we can work hard to pull it off again."
“For me, Van Hecke is ready. He's ready to play because he played under De Zerbi and he showed that he can play in the moment, that he's mature, and we need players that are already mature.”