The Albion and Holland centre-back is reported by David Ornstein via the Athletic to have been subject of an unsuccessful bid from Spurs as talks continue.
He was previously linked with his former boss Roberto De Zerbi at Tottenham, as were goalkeeper Bart Verbruggen and midfielder Carlos Baleba.
Van Hecke would appear to be the more pressing case for the Seagulls as he heads into the final year of his current contract at the Amex.
Spurs are expected to sign Bournemouth centre-back Marcos Senesi but De Zerbi is aware the squad needs major surgery and has spoken about imposing his preferred style of play over pre-season.
Former Spurs star Sandro told The Standard this week that he sees van Hecke as a great fit.
Sandro, who played for De Zerbi in Italy, said: “They are talking about Marcos Senesi, at Bournemouth, but I really like the defender from Brighton, Van Hecke.
“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.”
Van Hecke was one of three Albion players who started Holland’s send-off friendly against Algeria in Rotterdam last night.
But the occasion fell flat as they lost 1-0.
Verbruggen played the first half and Mats Wieffer, who was at right-back, was replaced on 69 minutes as Ronald Koeman made wholesale in-game changes.
But van Hecke was still on the pitch as Algeria scored their 86th-minute winner before then making way for striker Brian Brobbey.