A loan move for the former England captain had been described by Redknapp as a "no-goer" earlier in the day, but his tone changed after Tottenham's FA Cup third-round win over Charlton.
After a week of negotiations between Tottenham and Beckham's parent club, the Los Angeles Galaxy, Redknapp initially said that an eight-week loan for the star had fallen through because of "insurance issues".
Redknapp's assertion was followed by a statement on Spurs' website, announcing that the 35-year-old would join the club - but only to train for a month as he aims to keep fit during the MLS close season.
But following Spurs' 3-0 win against their npower League One opponents, Redknapp appeared to backtrack on his previous statement, and insisted the midfielder could still join.
When asked if a deal could still happen, the Spurs boss replied: "I don't honestly know. That's being done above my head. Hopefully it could still happen. The situation is ongoing."
Source: PA
Source: PA