Vertonghen, 25, has confirmed he plans to leave Amsterdam this summer to join a club in the Premier League, and his agent, Mustapha Nakhli, said Spurs were one of several clubs to have made a concrete approach.
However, while Redknapp is keen to sign the Belgium international, he says Spurs have yet to speak to Ajax about a deal.
"He is a good player, a player I have looked at and watched," Redknapp said. "I think there are a lot of clubs interested in him though. So, that is all.
"We haven't gone anywhere with it. We haven't spoken to the club. He is just a player I have watched, along with a lot of other players."
Ajax boss Frank de Boer believes Vertonghen should be aiming to secure a move to Barcelona.
"I hope he will leave for Barcelona," De Boer said. "Of course, Tottenham is a great club for Jan, but I think he will fit perfectly at Barca."
Ajax clinched the Eredivisie title on Wednesday night and De Boer is hopeful that he can keep the bulk of his squad intact.
"With age comes experience," he said. "You need that in a team, especially in the Champions League. If Van der Wiel and Vertonghen leave then that will be a big chunk taken out of the squad. Other players must stand up."