The former Senegalese international - once a teammate of Tim Cahill in China - departed Istanbul Başakşehir in April, having won a Turkish Super Liga title during his 28-month stay.
Ba, who turns 36 later this month, struck 20 goals in 59 appearances across all competitions, and as recently as December was in UEFA Champions League action against Paris Saint-German.
Ba has vacationed in Australia and previously hinted at an A-League odyssey when the time was right.
That time, according to his agent Ante Alilovic, could be now in what would be an undoubted coup for a competition crying out for a sprinkling of stardust.
Alilovic has already alerted several clubs - Melbourne Victory, Sydney FC and Western Sydney Wanderers are among them - and believes Ba would be the league’s biggest box office arrival since Alessandro Del Piero.
“Demba has had offers from the MLS but he’s had an eye on Australia for a while and would rather come to the A-League,” he said.
“I’m in discussions with several clubs and there’s no doubt he’d be a massive signing for any team here.
“He’s clearly still a potent force and he’s followed the A-League from afar for a couple of years.
“Demba would light up the league if a deal can be concluded.
“The competition has featured some big names over the years - but not too many in recent times. Demba would change all that.”
Ba, whose career has spanned England, France, Germany, Belgium and China, told Sky Sports recently: “I just want to enjoy my football for the last couple of years and find joy again.
"I would say there have been some things that have taken the joy of football away more or less over the last few years but I'm a lover of the game and want to finish on a very good note.
“It may end in another league, another country but I will make the best decision for myself and my family.
"I would have loved to have two careers - one where I just travelled the world and visited countries, cultures and learnt about people because I love to do that.
"But then I would have loved another where I stayed at one club for 10, 12, 15 years because it's special to do something like that.”
