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."
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.