Speaking after his side's 1-0 win over Fulham, Redknapp said he was looking to get Beckham to White Hart Lane as soon as possible, a move that would mark the former Manchester United star's Premier League return after nearly eight years abroad.
Due to Major League Soccer's summer season, Beckham is out of action while Europe's top leagues are in the thick of the action and he has previously joined AC Milan on loan in a bid to maintain his standards and keep his chances of playing for England alive. He tore his Achilles during last year's stint, however, forcing him to miss the World Cup and most of the MLS season, and Galaxy could be reluctant to let their star name and key player risk another spell on the sidelines as he edges towards his late thirties.
If Beckham does join Tottenham, he would be due to report back for Galaxy's new season in March, meaning Redknapp is eager to complete a deal sooner rather than later to allow Beckham to maximise his impact on Spurs' potential title tilt.
"He just said that he would like to come and play here at Tottenham,'' Redknapp said after his extended their unbeaten run to nine league matches. "We'd have to get him quickly if it's going to happen as he's only available until March. I've left it to the people at the club. I've passed it on them. They're talking to whoever they have to talk to at his club. It's down to whether they'd let him come or not."
Beckham previously stated that he would only return to the Premier League with United out of respect but they were not among the rumoured six or more clubs who were keen on securing his services. Tottenham would be the only one of the five clubs in the title race likely to be interested in Beckham, and since they have no direct rivalry with United and Beckham spent time at Spurs as a youth player, North London is a logical destination for a player keen to contribute at the highest level possible.
Redknapp said Beckham's previous declaration was now irrelevant, confirming: "David just said he'd like to come and play at Tottenham. He told me that."