Iniesta, 33, is set to leave the La Liga champions after 16 trophy-laden seasons with his boyhood club.
The Spain international was initially expected to move to China, but uncertainty surrounds his future, with Australia and Japan also mooted as possible destinations.
Gallop has confirmed that there are A-League clubs interested in Iniesta, while accepting there is going to be plenty of competition for the star's signature.
"I won't name who, but I do understand that A-League clubs have expressed interest and that's a start," he told a news conference on Thursday.
"He'll have offers from around the globe, but the A-League offers a great competition to play in.
"It also offers Australia's lifestyle and we saw with [former Sydney FC star Alessandro] Del Piero and others that that is an attraction."
Iniesta confirmed on Wednesday that "all possibilities are open", although he has ruled out a move to another European club.
Whether an A-League club could afford Iniesta is questionable and Gallop confirmed FFA, which reportedly has three million Australian dollars to use on marquee players, would only contribute to a portion of the star's wages.
"Of course the game has many mouths to feed and that will require a significant investment, primary from one of our clubs," he said.
"But we've got some funds available as well and if we can contribute – and it would be a contribution, it wouldn't be the bulk of what he could earn – then we think it's money well spent."