"In the past when that sort of name has been attached to this club, people considered it as something that was never going to happen.
"But cast your mind back to Youri Djorkaeff. People scoffed and said he would never come to play for Bolton but he came.
"So did Bruno N'Gotty, Ivan Campo and Fernando Hierro - we've attracted some fabulous players to the club.
"I am not saying that is going to get us Beckham but if it could, I would love it."
Allardyce is convinced, however, Beckham will stay put for the time being.
"I don't think David is considering leaving Real Madrid," he told Wanderers TV.
"He wants to do well and fight for his place because I know how much he loves the club and how much he loves Spain."