The Belgium international would prefer a move to White Hart Lane over a switch to Arsenal and hopes a deal can be concluded with the Dutch club holding out for a large fee
The Belgium international insisted that he trusts the move will happen, but revealed that the Dutch club are demanding a significant fee for his services.
Vertonghen pointed out that he would be able to walk away from the club for free in 2013, when his contract at the Amsterdam ArenA expires, so any stalling in negotiations are unnecessary.
"Tottenham are absolutely my favourite," Vertonghen told Dutch newspaper De Telegraaf. "[But] the Ajax board are asking for a very big amount for a player whose contract is running out in year.
"I trust that both Tottenham and Ajax will put some water in the wine and they will soon reach an agreement."
Vertonghen hoped his departure would not become so drawn out that it affected his reputation with the Ajax supporters.
The 25-year-old referenced goalkeeper Maarten Stekeleburg's move to Roma, which was not completed until August, as an example of how he hoped his departure would not be handled.
"I owe much to Ajax, but I've always given my whole heart and soul to the club," Vertonghen continued.
"My appreciation for the club and the fans is great. It would be terrible if my farewell is marred or distorted because Ajax [are stubborn] with the asking price.
"Of course I want Ajax to gain financially, but the amount that Tottenham want to pay, I think - perhaps with a little extra – is very reasonable.
"Next year I can leave for free. I hope that this awareness is there, because a transfer lingering for weeks like Maarten Stekelenburg's [to Roma] seems very harsh.
"He joined at the end of Roma's preparation [for the new season]. I want to be able to blend in with the other players at Spurs from the start [of pre-season training]."
Arsenal are also reportedly keen on the centre-back but Vertonghen pointed to Spurs' transfer policy as a reason for preferring White Hart Lane over the Emirates Stadium.
"Tottenham is a fantastic football club that has the tradition I want," Vertonghen explained.
"Ajax was the perfect club for me, but Spurs is already very close nearby. They buy young, eager, offensive-minded players."