The veteran midfielder is out of contract at the MLS outfit in November, making him a free agent, and the Loftus Park side want to bring him back to London.
Fernandes, who recently took over the ownership of the club, confirmed that he would like to see Beckham at Rangers.
“I think having someone like David in the club would be great. Was always in my thoughts. Let’s see,” he stated on his Twitter page.
Fernandes is known to be a shrewd businessman, and his investment has already funded moves for Joey Barton, Anton Ferdinand and Shaun Wright-Phillips.
However, the Air Asia chairman also has links from within entertainment company AEG, who own LA Galaxy, and is using this to start the negotiation process.
The former Manchester United man has previously stated that he would not return to the Premier League unless it was to Old Trafford, but despite this may be intrigued by one last chance to play in the top flight in England before his career ends.