Del Piero, 37, spent 19 years with Juventus but became a free agent in May and Sydney FC are keen to entice him Down Under to the domestic A-League.
"We're going to go for it as hard as we can," the club's chief executive Tony Pignata told the Sydney Morning Herald. "The board is 100 percent behind this. We believe he's the perfect marquee player.
"We've already made an approach to his management team, and we're waiting to hear back. This is not a gimmick, it's deadly serious. To get a player of his stature would be huge, and we know that," he added.
Del Piero has been linked to clubs in the Middle East and the United States, among others, but is yet to commit.
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