Beckham hopes to sort out a return to Europe on-loan next week.
Redknapp said: "We'll contact the LA Galaxy to see if they will let him go out on loan Turn to and if David is up for a three-month deal then we will definitely be interested.
"I'm sure he can still do a great job at the top level, otherwise I wouldn't bother.
"He would be a fantastic player to have here - and he wouldn't be coming just to sell some shirts."
The Spurs boss added: "He's a proper spot-on professional who would be a fantastic influence on everyone at the club.
"I'm not in a position where I need to get anyone in the transfer window. But I read Theo Walcott saying how he set a real example for him when he was training at Arsenal last year and you need people like that around your club."