The 37-year-old LA Galaxy midfielder remains one of the game's biggest names and his presence along with Italian superstar Alessandro Del Piero would help ratchet up the competition's global image.
FFA said Beckham's management had offered his services for the current season. Reports said he wanted to play a 10-game guest stint once the American Major League Soccer season ends in a fortnight.
"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," said an FFA spokesman.
"Beckham is a superstar on the world stage and he would be another massive signing for the A-League after the arrivals of Alessandro Del Piero, Emile Heskey and Shinji Ono. But this approach remains at a very preliminary stage."
The FFA said it was exploring all options available.
During his time with the Galaxy, Beckham has played against Sydney FC, Newcastle and Melbourne Victory in friendly matches.
However, a Beckham spokesman refuted the claim 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."