The two clubs are now in talks for the Belgium international.
Vertonghen has just one year left on his current deal and appears keen on a switch to the north London club.
The 25-year-old told De Telegraaf newspaper: "The board is asking a fair amount for a player who is only contracted for another year. I trust that Ajax and Spurs can turn water into wine and sort it out soon."
Vertonghen believes he would fit in nicely at Tottenham.
"Tottenham is a fantastic football club. Ajax was the perfect club for me, but Spurs will be very close in nearing that already. They buy young, eager and offensive-minded players."