The 27-year-old Belgium international, who has four years remaining on his current deal, has held preliminary discussions via his representative and hopes to put pen to paper as soon as possible.
Vertonghen's agent stated publicly earlier in the summer that a number of top European clubs were interested in the player, but Sky Sports reported in July that Tottenham would not sell their star centre-half.
Spurs did not receive any enquiries about Vertonghen during the window and the player is said to be optimistic about the season ahead under new manager Mauricio Pochettino.
Vertonghen's agent, Mustapha Nakhli, said: "We have spoken to Daniel Levy about a new contract for Jan and the negotiations were very good - we hope to sort everything out very soon.
"He is happy at Tottenham and wants to play for the club. He wants to play Champions League with Tottenham and he has a very good feeling about the new manager.
"Last year they made many changes and brought in many new players and it was not so good, but this season it is possible for Tottenham to qualify for the Champions League."
Vertonghen's future as well as that of goalkeeper Hugo Lloris has been of some concern to Spurs fans after the club finished sixth in the Premier League last season.
Tottenham have not made the Champions League since their only qualification under Harry Redknapp in 2010 - a failure that has seen the likes of Gareth Bale and Luka Modric seek top-level European football at Real Madrid.
Lloris signed a new five-year contract in July and Vertonghen is also expected to sign a long-term deal, but Nakhli warned he may reassess things should Spurs miss out on the Champions League once again.
"Playing at the highest level is, of course, very important for Jan," he said.
"If Tottenham do not qualify for the Champions League this year then we will have to see what happens next summer."