The 37-year-old 2006 World Cup winner was released by his former club Juventus in May and had been looking at options to extend his career outside Italy.
"Overnight we had two video conferences lasting about two hours discussing the possibility of bringing Alessandro Del Piero to Sydney FC for the 2012-13 season," Sydney FC chief executive Tony Pignata said.
"We spoke about football, as well as the Sydney lifestyle and the ability for him to leave a lasting legacy in the game.
"We presented him with what we think is a good package and we should get an answer within 48 hours."
Over 19 years at Juventus, Del Piero won six Serie A titles, two Coppa Italias, one Champions League and an Intercontinental Cup and would be the biggest ever name to play in the A-League.
British media reported on Thursday that Celtic manager Neil Lennon was hoping to bring Del Piero to Scotland before Friday's transfer deadline, while Swiss club FC Sion are also reported to have tabled a bid for him.
The new A-League season begins in early October.