Redknapp watched Saturday's 3-1 defeat at Manchester United from the stands and took training for the first time on Sunday morning after being installed as Mark Hughes' replacement.
QPR have taken only four points from their opening 13 fixtures and Redknapp has admitted there is no cash in the kitty to sign reinforcements during the January transfer window.
That points to a move for Beckham, who is preparing to leave Los Angeles Galaxy and would be a free agent, although his wages would likely be very expensive.
"I'm sure he could still play in the Premier League," said Redknapp. "He is a top player and a fantastic person.
"We had him at Tottenham training and he was amazing around the place, absolute class.
"I haven't discussed it with the chairman (Tony Fernandes) at the moment so we'd have to look at that.
"But David could still certainly be a great asset to anybody, showing people how to train, how to look after yourself. His professionalism is second to none."