The Los Angeles Galaxy midfielder was given the green light to start training with the Spurs squad after completing a series of fitness tests at the club's training ground in Chigwell, Essex.
"He's a fit lad, he looks like he's in great condition, looks like he looks after himself. He's a model professional so that won't be a problem. Whether it will be possible to do it (play for Tottenham), I'm not sure," Redknapp told Sky Sports News.
It is understood that Beckham is keen on playing for Spurs before returning to the Galaxy before their first match of the new Major League Soccer season against the Seattle Sounders on March 15.
As things stand, Beckham will only be at the club to train until February 10, but Redknapp has not given up on seeing the 35-year-old in a Tottenham shirt.
He continued: "It's great to have him here. We worked hard to get him here hoping that he could come and play.
"No-one could have worked harder than Daniel Levy, the chairman. They grafted away trying to get a deal done where he could play for us. It's a bit complicated but you never know. We'll see how it goes.
"They work on that side of it. I've got the easy part. I just identify people, say 'I'd like to get David - I think he'd be good for us'. It's up to them. They do the hard work and put the deals on."
Spurs have also been linked with a move for veteran Everton midfielder Phil Neville - Beckham's former Manchester United team-mate - but Redknapp described that prospect as "difficult".
"He's a great player but I'm sure David Moyes knows just how important he is to his team," said Redknapp. "He's a real leader for them and David wouldn't want to lose him so it'd be a difficult one."
Source: PA
Source: PA