Beckham, 37, will play for Los Angeles Galaxy in its Major League Soccer Western Conference final second leg against Seattle Sounders on Monday (AEDT) and may be involved in MLS final on Monday 3 December (AEDT), should his team, which holds a 3-1 advantage, progress.
In that event, he would be not be available to link up with an A-League club until at least Week 10 of the competition, which begins with Adelaide United's match against Melbourne Victory on Friday 7 December.
Any move is subject to financial backing by Football Federation Australia (FFA), with chief executive David Gallop required to sign off on a deal.
FFA confirmed it has received an approach by an agent representing Beckham's management with discussions at an early stage and the governing body exploring the options available.
"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," an FFA spokesman said.
"Beckham is 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."
Beckham is the third-highest earner in the MLS at $A3.9 million per season but is out-of-contract at season's end - he has already been linked with a move to New York Red Bulls.
It has been claimed the England star would be happy to take a significant pay cut to play in the A-League, but it won't be at Melbourne Victory.
"That's great if he is coming," Victory coach Ange Postecoglou said. "Would we be interested? Nah".
Western Sydney Wanderers executive chairman Lyall Gorman told Fairfax: "No one has approached us about it.
"If we were to be approached, we would go through the normal process. We've had no approaches at all and we don't speculate on those things until they come across our table."
Perth Glory was recently linked with a move to sign Harry Kewell, but its chief executive Paul Kelly said the club hadn't been contacted by Beckham's people.
"I don't know anything about it. I know he's being touted around, but there's been no conversation," Kelly said.
"We are always happy to speak to players of the calibre of David Beckham, who would be great for the Hyundai A-League as illustrated by the effect of Alessandro Del Piero, Emile Heskey and Shinji Ono. "At the end of the day it's the coach, Ian Ferguson who makes these decisions and we as a club, have a process that we follow when recruiting players. "But we would be mad not to seriously consider David Beckham."
Sydney FC, Western Sydney Wanderers, Melbourne Heart and possibly Brisbane Roar are considered the most likely destinations for the international football icon.
Beckham has spent two MLS off-seasons in Italy's Serie A with AC Milan and has previously played against Sydney FC, Newcastle Jets, Melbourne Victory and Wellington Phoenix in exhibition games with Galaxy since his first visit to Australia in 2007.
