The defender has previously hinted he would leave if Spurs weren't able to secure qualification for the Champions League - an objective they fell well short of this season.
According to the Telegraph, the Belgian, who has been named as part of his country's World Cup squad for the tournament in Brazil next month, would have been willing to quit had Tim Sherwood been retained as Tottenham manager.
However the 45-year-old was let go this week having taken over from Andre Villas-Boas, the man who took Vertonghen to Spurs, in December.
Current favourite for the job is Southampton boss Maurico Pochettino, ahead of Ajax manager Frand de Boer, who oversaw Vertonghen's development while he was with the Amsterdam club, prior to his move to Tottenham in 2012.
Previous reports suggest that Spurs are keen to hang on to the 27-year-old and will offer him a new contract to keep him from the likes of Barcelona and Roma.