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.
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.
"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.
Source: PA
Source: PA