Spurs and Ajax have been locked in negotiations over the transfer of the 25-year-old Ajax captain, who impressed during Belgium's 1-0 defeat to England at Wembley last Saturday.
Ajax's valuation of the centre-back, reported to be 15million euros, had proved to be a sticking point, though, as the Londoners are not willing to pay that much for a player whose contract expires next summer.
Vertonghen last week said Spurs' failure to qualify for the Champions League would not put him off a move to White Hart Lane and Mustapha Nakhli, who represents the towering Belgian, is hopeful a deal will be concluded soon.
"Jan is waiting. The clubs are close," Nakhli told Voetbal International. "I hope it will be this week. I think it will. We are talking to Tottenham."
Nakhli appeared to criticise Ajax for holding out for a bigger fee than Spurs are offering. He added: "Fifteen million? Jan has a contract until mid-2013. So what do you think?"
The addition of Vertonghen, who can also play at left-back or in midfield, would be a big boost for manager Harry Redknapp, who had to consistently change his back four last term due to a number of injuries.
Michael Dawson only played 13 games, William Gallas struggled with a niggling calf injury and Ledley King may be forced into retirement after his chronic knee problems surfaced again towards the end of the season.
Redknapp is determined to land a striker and perhaps another top-class player to freshen up his squad, but the main focus this summer will be keeping Gareth Bale and Luka Modric at White Hart Lane.
One player who has been sidelined due to the emergence of the sought-after pair is midfielder Niko Kranjcar. The Croatian made just nine Barclays Premier League starts last season and appears to be heading to Ukrainian side Dynamo Kiev. Kranjcar told Croatian website Jutarnji List. "The clubs have agreed."