LOS ANGELES - According to FFA officials, the approach was made in relation to Beckham playing in the A-League during the current 2012-13 season.
"The approach from David Beckham's people is another sign of how much the A-League has grown in stature on a global basis," the FFA said in a statement.
"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."
The statement added that talks with the former Manchester United and Real Madrid midfielder were at a "very preliminary stage."
The 37-year-old Beckham, currently with the LA Galaxy, is interested in a 10-game deal at the conclusion of the Major League Soccer season, according to Australian media.
Beckham's Galaxy, reigning Major League Soccer champions, face the Seattle Sounders next week in the second leg of their Western Conference final after winning the home leg 3-0.
Beckham is out of contract at the end of the MLS season in December and has already been linked with the New York Red Bulls by American media, who speculate the move would allow his former popstar wife Victoria to pursue a fashion career.
Despite the FFA's disclosure, three Australian clubs distanced themselves from Beckham, arguably the most recognisable sporting celebrity in the world and one of the highest-paid.
"That's great if he is coming," Melbourne Victory coach Ange Postecoglou told local media. "Would we be interested? Nah."
Western Sydney Wanderers executive chairman Lyall Gorman told Fairfax Media: "If we were approached, we would go through the normal process.
"We've had no approaches at all. We don't speculate on those things until they come across our table."
Perth Glory denied any contact had been made but chief executive Paul Kelly said: "We would be mad not to seriously consider David Beckham."
Former internationals Del Piero, Heskey and Ono have all recently joined A-League clubs, the Italian, Englishman and Japanese boosting the profile of soccer Down Under.
Sydney FC, Western Sydney, Melbourne and Brisbane Roar are considered the most likely destinations for Beckham, local media reported.
The Central Coast Mariners currently lead the 10-team A-League after six matches of the season.
Beckham has spent two MLS off-seasons in Italy's Serie A with AC Milan and almost joined England's Tottenham Hotspur on a similar two-month loan in January.