The World Cup winning forward has rejected the overtures of the Swiss outfit and will now mull over a big money deal to move to Australia over the next 48 hours
The A-League club's CEO Tony Pignata had two video conferences with Del Piero's representatives on Wednesday, lasting around two hours, and he has reportedly offered the 37-year-old a deal worth $2 million (€1.6m) to join Sydney FC.
Del Piero had been involved in negotiations with FC Sion earlier this week but has reportedly rejected a move to the Swiss Super League club, putting Sydney FC in a much better position to lure the Italian striker to Australia.
"We spoke about football, as well as the Sydney lifestyle and the ability for him to leave a lasting legacy in the game," Pignata said on Thursday.
"We presented him with what we think is a good package and we should get an answer within 48 hours."
Sydney FC have only come into the market for Del Piero after former marquee player Nicky Carle was allowed to leave the club on loan to play in the United Arab Emirates with Baniyas.
That move opened up a marquee spot, which would allow Sydney FC to pay Del Piero outside their salary cap. Pignata moved quickly, confirming the club's interest in the veteran forward on Wednesday.
Del Piero would arguably become the highest-profile marquee the A-League has ever had, surpassing Dwight Yorke, Robbie Fowler and Harry Kewell.
"Alessandro Del Piero is one of the true legends of football and there is no doubt that if he was to come to Sydney FC it would be huge, not only for our club and the Sydney football community, but for the whole A-League," Pignata said.
Even though Del Piero has seemingly rejected Sion, Sydney FC still have rivals for his signature, with Tottenham Hotspur and Celtic both having offered him contracts, according to the Italian media.
Del Piero played 513 league games for Juventus in 19 seasons with the Serie A club, scoring 208 goals. He also scored 27 times in 91 appearances with the Italian national team.