The former Spur and Liverpool midfielder has worked with our recent signing at close quarters at Anfield and says, despite interest from other clubs, Jamie was always very keen to head to White Hart Lane.
"It wouldn't surprise me, as soon as he starts playing and gets a few games under his belt for Tottenham, if he forces his way back into the England set-up," said Nicky.
"It would be good for him and I'm sure it's in the back of his mind. I know for a fact that he wanted this move, there were a few clubs in for Jamie but he wanted to come to Tottenham.
"Glenn Hoddle, I know, likes him very much as a player. Jamie will respond well to Tottenham and do very well."
Jamie, of course, was club captain at Liverpool and Barmby says he is a great leader and a player in the Tottenham tradition that he feels Spurs fans will appreciate.
"He is, he's a very nice man first and foremost. As a player he is just in the Tottenham tradition, he's a great footballer who'll do very well here.
"He is a great passer. The fans here, I know more than most, appreciate good football and Jamie will bring that."
Jamie has had his problems with injuries over the last couple of season and Barmby says, even during such a long spell, his professionalism never dipped.
"A very, very good player. He's been out two years and his professionalism in that two years was fantastic.
"I caught the back four or five months of when he was out after my operation. He is a fantastic player."
Barmby's thoughts were echoed by fellow midfielder Gary McAllister. The veteran Scot, soon to be manager of Coventry, hopes we get a new Jamie Redknapp, one clear of injury that he says is one of the best in the country.
"Hopefully it's a new Jamie Redknapp," said McAllister. "Everybody knows he's had a horrendous time with injuries.
"Everybody at Liverpool wishes him well and a clear run with fitness now.
"Hopefully he can get his career back on track now. There is no doubt about it, a fit Jamie Redknapp is one of the top ten midfield players in this country.
"He's proved over the years what a class player he is, he's just been very unlucky with injuries. I just hope he can get a clear run and stay clear of injuries now."
By Richard Hubbard
Nicky Barmby has tipped Jamie Redknapp for an England recall once his Tottenham career gets fully underway next season.