The LA Galaxy midfielder will instead train with Spurs for a month until February 10, when he will return to the United States to prepare for the start of the Major League Soccer (MLS) season.
"I don't think (a loan deal) will happen - there's a big problem with the insurance," Redknapp told Sky Sports television.
"David is welcome to come and train with us for a month, which I think he would like to do. But as for him playing - it's looking like a no-goer."
Beckham told the Spurs website: "It's important that I maintain a high level of fitness during the MLS off-season.
"I'm thankful to Tottenham and Harry Redknapp for giving me the opportunity to train with the team over the next month. I'm grateful to the LA Galaxy for allowing to me to train with Spurs. I look forward to getting to work as soon as possible."
"David is a fantastic professional - he will be a great influence around the place and I am sure we will all benefit from his winning mentality," Redknapp said on the Spurs website.
"I think everyone will enjoy having him here. We'd love to have him here for longer but respect his commitments to LA Galaxy. They wanted him back in early February so that made it difficult to do a playing deal on the basis of three weeks."
