The Spain international was linked to Chinese side Chongqing Dangdai Lifan but no deal has materialised and media reports now speculate the midfielder might head to Japan or the United States.
J-League side Vissel Kobe's head of player development Atsuhiro Miura, however, has denied that Iniesta had agreed to join the Japanese team owned by Barcelona's sponsor Rakuten, leaving room for Australian clubs to make a move.
"I won't name who but I do understand that A-League clubs have expressed interest, and that's a start," Gallop said on Thursday.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"He'll have offers from around the globe but the A-League offers a great competition to play in and the Australian lifestyle... is an attraction.
"It would require a significant investment, primarily from one of our clubs, but we've got some funds available as well and if we can contribute - it would be a contribution, not the bulk of what he could earn - then we think it's money well spent."
According to Australian media reports, Sydney FC, Melbourne Victory, Newcastle Jets and Western Sydney Wanderers are interested in using the FFA's A$3 million ($2.24 million) war chest to sign Iniesta.
"I said that I would not go to Europe and apart from that all possibilities are open," Iniesta told beIN Sports after Barcelona's 5-1 victory over Villarreal on Wednesday.
"You will know when I tell you. There are things to seal, little details and I will try and choose the best option."
Iniesta is expected to play his last two matches for Barcelona in their season-ending La Liga fixtures against Levante and Real Sociedad.
($1 = 1.3396 Australian dollars)
(Reporting by Aditi Prakash in Bengaluru; Editing by Amlan Chakraborty)
