The 33-year-old has rejected Chinese side Chongqing Lifan and is understood to prefer a move Down Under for the lifestyle and an up-and-coming league, says Spanish newspaper Sport.
Iniesta decided to leave Barcelona after 22 seasons with the club, winning an extraordinary nine La Liga titles and lifting the UEFA Champions League trophy four times. He also won the 2010 World Cup with Spain in 2010.
Australia has proved a destination for some of football elite over the years with Dwight Yorke, Alessandro Del Piero and David Villa enjoying stints in the A-League since it's inception.
It's likely Football Federation Australia would help fund an Australian club's move for Iniesta, with powerhouses Melbourne City, Melbourne Victory, Sydney FC and Western Sydney Wanderers likely to be in the frame if the Spaniard is available.
J-League club Vissel Kobe is also interested in the signing of Iniesta, while several other clubs in Asia are likely to be keen for his services now that's it emerged he is unlikely to move to China.
Over 16 seasons of first-team football at Barcelona, Iniesta made 437 appearances, scoring 35 goals.
He has 125 international caps for Spain and has hit the back of the net 13 times.