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.
Beckham's contract with the Galaxy expires in November and Redknapp said: "What are the chances of us signing him? I have no idea."
He added: "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 on Friday 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."
Source: PA
Source: PA