Amit Bhatia is considering extending an offer to the former England captain but believes that the player may prefer a move to White Hart Lane if given the chance
Beckham has been strongly linked with a move to Neil Warnock's side at the end of his MLS contract in November, however, QPR face competition from Tottenham for his signature.
"Would we be prepared to offer him a chance to play for QPR? The answer to that question is yes, we would be willing to make him an offer," Bhatia told The Daily Mail.
"It’s something Tony and I have discussed and we would throw our hat into the ring for someone like him.
"It’s up to Beckham — or any other player of that calibre — to decide whether he wants to join QPR, I’m not certain Beckham would want to join a newly promoted club.
"If he wanted to come to London maybe he would choose Tottenham."
QPR showed a good deal of ambition in the transfer market following Tony Fernandes' takeover, signing players such as Joey Barton and Shaun Wright-Phillips.