The game's new boss said a similar situation arose earlier this year when Alessandro Del Piero's camp tried to distance themselves from speculation linking him to Sydney FC.
Speaking on Triple M's The Dead Set Legends, Gallop said it was natural for stars to want negotiations kept out of the limelight and urged A-League clubs to be proactive and persist with negotiations.
"A similar thing happened with Del Piero in terms of the contact and, as we all know, that came to be. So let's just see how this one plays out. It's certainly an exciting proposition - no one would deny that," said Gallop.
"We're not counting our chickens in relation to this ... but obviously people would prefer negotiations to happen behind closed doors.
"At the mere mention of Beckham's name, it did leak out and there's been a mushroom of interest.
"There would have to be a fair few hoops that would have to be jumped through and getting a deal with one of the clubs is the first step.
"There's definitely been some contact made and let's just see where it gets to."
Gallop said clubs needed to take the initiative with negotiations and not rely on the FFA and said patience would be needed.
"I think the connection points now are going to be between the A-League clubs that are interested and Beckham's management, so we'll just have to let that dialogue happen.
"But the timing is pretty good in terms of him being able to come in on a guest stint from the middle of January for 10 games. I think it's a bit of a wait-and-see situation. Of course, it would be fantastic but let's not get ahead of ourselves at this point."
-AAP