Spurs and Beckham's parent club, the Los Angeles Galaxy, have been locked in talks all week and the former England captain is thought to be keen on a move to the north London club.
Is that the way to White Hart Lane? Beckham looks set to join Tottenham on loan
Redknapp says there is a 'good chance' a deal will happen for Beckham and hopes the 35-year-old will come to watch the club's FA Cup third round match against Charlton on Sunday.
'I think he could be here on Sunday possibly if what I'm being told on the grapevine is right,' said the Spurs boss.
'The clubs are talking and there is a good chance it will happen.
Harry heard it through the grapevine: Redknapp is keen to bring Beckham to Tottenham
'Hopefully he will come to the game, I'm sure. I'm not 100% sure but he could be here on Sunday.'
If Beckham's arrival is secured this weekend, he could go straight into the squad for Spurs match against the midfielder's former club Manchester United the following Sunday.
Negotiations began over a loan deal forBeckham last weekend after Redknapp revealed his son, Jamie, had talkedto the former Real Madrid man about a loan deal during the MLS closeseason.
On the ball: Redknapp lauded Beckham's crossing ability
The Spurs boss warned the Americanside earlier this week that a deal would have to be sorted out soon asthe Galaxy are thought to be keen for Beckham to return for the startof the new season in March, which would give the star around only eightweeks at White Hart Lane.
Redknapp is now confident the dealwill go ahead though and is convinced that Beckham will provide anability to cross the ball that was lacking in the Londoners' 2-1 defeatto Everton in midweek.
'I wouldn't bring him here if Ididn't think he had something to offer,' Redknapp said. 'We're nottalking about long-term but I'd love to have him around the place.
'He would lift the level of theother players, people would respond to playing with him and having himaround and he would be a good influence around the place.
'He could be a massive player for us. 'He has the ability to do some of the things that we don't do well.
'The other night we played PeterCrouch up front. Alan Hutton hits him with one great ball, he heads theball down and Rafa van der Vaart scores.
'Other than that he (Crouch) didn'tget too many opportunities because we didn't put the ball where weshould be putting the ball .
'David Beckham has that ability to drop the ball on his head 19 times out of 20 and that's important.'
Beckham is thought to prefer a move to Spurs, with whom he trained as a youngster, over several other offers from around Europe.
The midfielder thinks a move to Spurs could re-ignite his England career after being overlooked by England coach Fabio Capello since the end of 2009.
Reports earlier this week suggested that Beckham and Redknapp had been lined up to replace Capello when the Italian's tenure as Three Lions boss ends in 2012.
Redknapp rejected those claims today, however. 'I don't know where that has come from. There's nothing in that whatsoever,' Redknapp said.
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