Beckham has announced he is leaving Los Angeles Galaxy with Paris Saint-German and clubs in Australia reportedly leading the chase to sign him. In early 2011 the 37-year-old trained at Tottenham Hotspur when Redknapp was the manager.
Asked if there was interest in taking Beckham to QPR, he told BBC 5 Live: "I'm sure he could still play in the Premier League. He is a top player and a fantastic person as well. I must admit we had him at Tottenham training and he was amazing around the place – absolute class. I've not discussed it with the chairman at the moment so we would have to look at that. David could still certainly play and still be a great asset to anybody, just having him around the place, showing people how to train and how to look after yourself. His professionalism is second to none."
Redknapp played down any major recruitment drive in January. "I think they bought a lot of players in in the summer – I think it was 12 signings – so I don't see a lot more coming in in the window," he said. "You can't just keep loading up the squad with more and more players and if things don't go right you are going to end up in big trouble financially. So I think we are really maybe looking at one or two loans in January. But there's a decent enough squad here.
"For whatever reason something's wrong. The manager is the one who has suffered, Mark's lost his job, but to have four points from 13 games is pretty horrendous and the players have really got to take responsibility."
While players may need to be let go to generate funds for Redknapp, who took his first training session on Sunday morning, it is understood Fernandes will provide some money to strengthen the squad.
Redknapp may consider returning to Tottenham to revive the deal for Michael Dawson, his former captain there. Dawson came close to joining in the summer but terms could not be agreed. A loan or permanent move for Dawson's team-mate Tom Huddlestone could also be an option, while Redknapp may make an enquiry to Aston Villa about the out of favour Darren Bent.
Redknapp began his tenure as Mark Hughes's successor by watching as QPR were beaten 3-1 by Manchester United at Old Trafford on Saturday afternoon.
Of their chances of survival Redknapp added: "Let's hope it's upwards. The players have got to be responsible at the end of it all and we've got to get cracking quick."
Redknapp stated he came close to becoming the Ukraine manager. "Despite what everybody might think," he said, "I was genuinely interested in the Ukraine. It was a job that would have allowed me to commute between England and the Ukraine. It's only a two and a-half-hour flight, there's two flights a day out of London. It would probably have meant going over three or four days a week and watching games at the weekend, having a few days at home as well. It was a great job. But having this come up – the Premier League is special – so I thought 'let's have a go and take it on.'"
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