Barber has made it clear that neither offer came close enough to the £70m valuation the south coast club have placed on the 25-year-old Netherlands international.
Barber spoke to talkSPORT, becoming the most senior club figure to address the pursuit directly.
"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. 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, because he's got another big season ahead of him."
He framed the decision in the context of the club's dual ambitions.
"He's had two seasons in the Premier League and 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."
Van Hecke has one year remaining on his contract and has declined to sign an extension — a position that will reduce Brighton's bargaining power as the summer progresses. Tottenham, Chelsea and Liverpool have all been linked, with the defender's existing relationship with Roberto De Zerbi from their shared time at Brighton considered a significant pull factor toward the Spurs move.
Van Hecke started for the Netherlands in their 1-0 friendly defeat to Algeria last week, with the World Cup now an additional variable that could affect his valuation and desirability once the tournament concludes.