The Belgian has been heavily linked to the club for a number of weeks but a deal appeared to have stalled over a clause entitling the player to 15 per cent of any transfer fee
The 25-year-old's future has been the subject of intense speculation since he expressed a desire to leave the Dutch giants, but matters finally appear to be coming to a head.
Vertonghen, who has also been linked with Spurs' north London rivals Arsenal in the past, had hoped that his transfer would be sealed by now, but returned to pre-season training at Ajax this week with no deal yet assured.
One major factor in the transfer discussions is Vertonghen's entitlement to a percentage of the transfer fee.
The Belgian believes that he is due around 15 per cent of the overall sum, believed to be around £9 million, but Ajax are holding firm, leaving Vertonghen in the lurch regarding his move to White Hart Lane.
There have even been suggestions that Vertonghen may seek to play out the final year of his contract before sealing his dream move to Spurs on a Bosman free next summer.
All parties would sooner see a conclusion reached now, with a spokesman for Nakhi Mondial - Vertonghen's management agency - saying: "We have nothing agreed at this moment.
"The talks were not easy but we are going to try again, maybe on Saturday."
If the deal goes through it would be seen as something of a coup for Spurs, who have snapped up Gylfi Sigurdsson and Manchester United's Ezekiel Fryers to add to the appointment of new manager Andre Villas-Boas this week.