This week's sacking of Redknapp, who wanted to sign the player in January, raised doubts over whether the deal would go ahead, but Vertonghen's agent Mustapha Nakhli insists the move is "very close".
"Nothing has changed at all. He is coming to Tottenham for the club and not for the manager," Nakhli said.
"Managers come and go. Of course Jan is sorry that Harry Redknapp is no longer there but he is going for the club.
"We have a good relationship with Daniel Levy. He wants the deal to happen and there is a good atmosphere (between us).
"I don't know when it will happen but the deal is close, very close."