Beckham trained with Spurs in January during the Major Soccer League's close season in order to keep fit, and the London club were keen to sign the former England captain on a short-term deal, but negotiations broke down and Beckham returned to his parent club, the Los Angeles Galaxy.
But Beckham's contract with the Galaxy expires in November and he could decide to come back to England for one last crack at playing in the Barclays Premier League.
QPR's new owner Tony Fernandes wants to sign the player, but Tottenham would be a much more attractive option for Beckham given that they are able to offer him the chance to play in a team likely to be challenging for a top-five position come the end of the season.
Redknapp has never hid his admiration for Beckham and admitted this morning that he would "love" to sign the 36-year-old, who moved to the United States in 2007.
The Spurs boss insisted this afternoon that no talks had been held between the two camps, though, and admitted that any potential signing was a long way off.
"What are the chances of us signing him? I have no idea," Redknapp said.
"I'll be honest. I don't have a clue. I wouldn't know the financial situation or what it would take. I have never discussed it with the chairman.
"Would I like him here? Of course I would.
"I don't think you would ever say no to David Beckham. He would bring a lot to any club.
"He came and trained with us last year. He was fantastic to have around the place as a player and as a person.
"He was a top-class professional and he's the kind of lad you would like around the place. He is someone the young lads look up to and he is a great role model for anybody."
Luka Modric returned to Tottenham for the first time since the transfer window closed, ending any chance of him moving to Chelsea, until January at least.
Redknapp admitted two weeks ago that the protracted transfer saga had taken its toll on the Croatian and the rest of the Spurs squad.
The Tottenham manager insists he has no qualms about the 25-year-old giving his all for the club for the rest of the season, but thinks the midfield star would be much happier if he had completed his move to Stamford Bridge.
"I could sit here and say: 'yeah, he's glad he never went to Chelsea, he's glad he didn't get all that money, he is much happier now' (but) I would be talking rubbish," Redknapp said.
"I don't know how he feels but he is here and we get on with it now."
Redknapp admitted that he was willing to let the Croatian leave after the player fell out with Spurs chairman Daniel Levy and went public with his request to leave.
"I had always been brought up with the belief that if you didn't want a player you would move them on and bring someone in who does ," Redknapp added.
"I was of that opinion in the end. I thought: 'If Luka doesn't want to be here then take £40million and we'll all move on.' But I love him as a player. I'm delighted he's still here."
Levy succeeded in keeping hold of Modric and supplying Redknapp with two new signings in Scott Parker and Emmanuel Adebayor.
Redknapp hopes the pair, who will start Saturday's game at Wolves, will be able to give the squad the boost it needs after two humbling defeats.
"I felt we needed to keep Luka and add to him," Redknapp said.
"It will give us a big lift having those two here."
Redknapp revealed that Rafael van der Vaart is making good progress in his recovery from a hamstring tear he suffered against Manchester City.
The forward has been having treatment on the injury in Holland and Redknapp thinks the player will be back "much quicker" than the six-week period he originally thought he would be out for.