The 25-year-old defender showed his versatility - one of the attributes which has impressed Redknapp - with a solid display at left-back for Belgium in Saturday's 1-0 friendly defeat against England at Wembley.
Quoted in The Sun on Sunday, the Spurs boss said: "Jan is a terrific passer and versatile too. He can play at the heart of defence but also plays very comfortable at left-back.
"I hope a deal is done but I don't think it's quite finished yet."
The player revealed on Friday night he was close to joining the north London club, claiming a deal could be done in the next "couple of weeks or maybe days".
Vertonghen, who has also been linked with a move to Tottenham's arch rivals Arsenal, said: "I am a big fan of the Premier League. It is almost the only competition I watch on TV and for me it is the best competition in the world.
"I would like to play in the Premier League. I am not in contact every day but I think it could be very close now, maybe a couple of weeks or maybe days.''
Asked if he knew which club he wanted to join, he said: "I probably know which team I will be going to, yes. I know where I want to go and I think it is clear to everybody."
When probed as to whether that club was Tottenham, he nodded and said: "Yes."
Rafael van der Vaart has insisted he wants to stay at Tottenham, although he refused to entirely rule out a move to Schalke.
The 29-year-old former Hamburg midfielder has been linked with a return to Germany, where his wife still works.
Asked about the prospect of joining Schalke, Dutchman Van der Vaart told Bild: "I don't know. Actually, I want to stay at Tottenham. But, in football, you never know."
Pointing out he never expected to join Spurs or Real Madrid in the way he did, he added: "I spent three years living in Hamburg and had a wonderful time at HSV.
"My wife, Sylvie, works there and we have many friends who live in your country."