The 36-year-old midfielder trained with Tottenham during the last MLS off-season and manager Harry Redknapp is interested in signing him in January.
"I don't think you would ever say no to David Beckham. He would bring a lot to any club," Redknapp said Friday. "He came and trained with us last year. He was fantastic to have around the place as a player and as a person.
"He was a top-class professional and he's the kind of lad you would like around the place. He is someone the young lads look up to and he is a great role model for anybody."
Although Beckham trained with Spurs in January, the club failed to agree a loan deal for the former England captain.
And talks are yet to start between Spurs and Beckham's representatives ahead of the MLS season ending in November.
"What are the chances of us signing him? I have no idea," Redknapp said. "I'll be honest. I don't have a clue. I wouldn't know the financial situation or what it would take. I have never discussed it with the chairman.
"Would I like him here? Of course I would."
QPR's interest in bringing the former Manchester United and Real Madrid player to the Premier League newcomers emerged in a tweet from owner Tony Fernandes.
"It is not a discussion chairman Tony Fernandes and I have had," QPR manager Neil Warnock said.