The midfielder has made a memorable start to his Spurs career after joining us at the back end of last season.
He marked his first home game with one of the best goals seen at the Lane in years against Lazio, impressed in his competitive debut with his first 90 minutes for us at Everton and, on Saturday, netted another sweet volley to grab the points against Aston Villa in his first Premiership game at home.
Boss Glenn reiterated his claim that Jamie could be the 'buy of the decade' and, at his best, likened him to David Beckham.
It's a far cry from the well-documented injury misery the 29-year-old has suffered in the last few years. Indeed, his goal and games against Everton and Villa were his first since last October.
Glenn explained: "Jamie's a great passer of the ball and the club has been brought up with traditions of players like that.
"I think Jamie is as good a passer as there is in the country.
"He's up there with David Beckham at his very best. He's still a way to go to get back to that very best, it might take another six months to be consistent. But if he gets back to his best then he's up there.
"The injuries look okay. They have to be managed and we'll have to look after him at times, but as I said when he got here, he could the buy of the decade, or non-buy, as he didn't cost anything.
"I'm convinced, not hopeful, that in the next two or three seasons we'll see him back to his best.
"He deserves that. He's what a call a diamond lad, a great character. The cards he's been dealt, well, he's deserved better."
It was pointed out that Jamie's problems would have made him hungrier to succeed in his new start at Spurs.
Glenn agreed. "He's already proved he's got that desire with his first 90 minutes at Everton.
"I was surprised because I thought I would have to bring him off at some stage but he showed character and grit to get through it. He's grown in staute.
"Injuries make you strong, without doubt, more resiliant, make you deal with things and cope with adversity because there is nothing more frustrating for a footballer I can assure you than being injured.
"If you are going through bad form that can be changed and that's part of you as a player.
"But when you are injured, you can't play and you are stuck in that treatment room, that is the worst place to be.
"I think Jamie is very happy. He's happy with his envirmonment, where he's living, happy that he's come to a club that passes the ball and will appreciate his skills.
"He's a fit lad, looks after himself and the way he plays, he could play until he's 37, 38, because he lets the ball do the work."
TICKETS FOR SPURS V SOUTHAMPTON ON SATURDAY AUGUST 31 NOW ON GENERAL SALE - CALL 08700 112222 OR
CLICK HERE FOR DETAILS
Glenn Hoddle believes Jamie Redknapp will get better and better.