Beckham signed a new two-year contract with the Galaxy in January, but has previously had two loan spells with AC Milan during Major League Soccer close seasons.
And Football Federation Australia (FFA) released a statement early this morning in which it said it had been approached by the Beckham camp with a view to the player spending a short stint in the A-League.
A Beckham spokesman was quick to refute the claim, however, describing it as "rubbish" before adding in a statement: "There is always enormous interest from clubs across the world in signing David as a player.
"There are absolutely no plans to play in Australia, David is completely focused on the MLS play offs and winning another Championship with the Galaxy."
That stance contradicts the signals emanating from Australia.
The FFA statement read: "The approach from David Beckham's people is another sign of how much the Hyundai A-League has grown in stature on a global basis.
"Beckham is a superstar on the world stage and he would be another massive signing for the Hyundai A-League after the arrivals of Alessandro Del Piero, Emile Heskey and Shinji Ono. But this approach remains at a very preliminary stage."