However, he has been training with Spurs to keep in shape during Major League Soccer's (MLS) off-season.
"David Beckham will now return to Los Angeles to report for pre-season training with LA Galaxy on 24 February," said Tottenham.
One of the stumbling blocks in Redknapp's bid to acquire the former England captain on a short-term basis was believed to be Galaxy's earlier insistence that he return to them by 10 February ahead of their MLS opener away to Seattle Sounders on 15 March.
"To do [a loan deal until 10 February] would be a waste of time because, by the time David got fit, it would be a couple of weeks and suddenly you'd be into February," Redknapp said last month.
Beckham's Galaxy contract expires in November, when Redknapp may again revive his interest in signing the 115-time capped England player.
The last of those caps came on 14 October in the 3-0 World Cup qualifying win over Belarus at Wembley.
However, after been ruled out of the World Cup with an Achilles injury, Beckham has not given up on playing for England again, and had been hoping to catch the eye of England manager Fabio Capello with a two-month spell in the UK.
Beckham, who had also been linked with loan switches to Everton, Leicester and Newcastle, has plied his trade abroad since
leaving Manchester United for Real Madrid
in June 2003.
Source: BBC Sport
Source: BBC Sport