However, Redknapp will need all his powers of persuasion to convince Beckham to snub lucrative offers from Paris Saint-Germain , Qatar, Brazil, China and Russia to join the QPR relegation battle.
He wants Beckham to give the club the biggest boost possible by agreeing to finish his playing career at Loftus Road, the Daily Mirror reports.
According to the report, Redknapp's bid to sign Beckham on a free transfer will be backed by QPR owner Tony Fernandes, who attempted to sign the former England captain last year.
The new QPR boss has also targeted January moves for Spurs duo Michael Dawson and Emmanuel Adebayor, the report said.
Redknapp tried to sign Beckham on loan for Spurs in January 2011, but the midfielder was only able to train with the club. Beckham's attitude has reportedly impressed Redknapp and he sees the 37-year-old's experience as a key ingredient to helping QPR stay up, the report added. (ANI )