Beckham is ready to return to England on-loan from LA Galaxy.
While Redknapp has yet to speak personally to the 35-year-old, he has been informed of Beckham's desire to move to the club where it all began for the world's most famous footballer.
"He just said that he would like to come and play here at Tottenham," Redknapp said.
The final decision over whether he joins Tottenham, however, lies with the Galaxy and Redknapp admitted the north Londoners would need to move quickly.
"We'd have to (move quickly)," said Redknapp, who revealed the job of persuading the Los Angeles club lay with director of football administration Darren Eales.
"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."
Redknapp insisted that far from being a luxury acquisition, Beckham would provide much-needed cover for right winger Aaron Lennon.
"We've got no-one else to play on the right," he said. "David Bentley keeps picking up injuries on Friday morning.
"It's a no brainer."
Redknapp admitted Tottenham could have done with Beckham as they ended their London derby with Fulham clinging on to their 1-0 lead.
"He could've come on when we were under pressure," he said. "He might've kept the ball for us.
"When I took Teddy Sheringham to Portsmouth, I used to just say, 'Watch him train. Watch everything he does. He does it 100% right.'.
"And I think Beckham's like that. They tell me after training, he spends an hour out there practising.
"If young players see that, it's better than all the coaching in the world."