The former Juventus great joined the club in September, making the 2006 FIFA World Cup™ winner the biggest signing in the domestic A-League history.
The lucrative deal, reportedly worth €1.6 million (US$2 million) a season, was for one-year with another one-year option.
He told journalists talks had taken place between his management and the club about staying on but the situation had turned into a waiting game.
"We have been talking. We are waiting (for) what it (the club) decide ... they wait (for) me. Everybody is waiting," Del Piero told The Australian.
"We have discussed things. We have a good relationship, but at the moment we have to think day by day."
Sydney FC chief executive Tony Pignata, who was instrumental in bringing Del Piero to Australia, confirmed the player wanted to take up the extra year option.
"We had preliminary discussions a few weeks ago and Ale indicated he was keen to stay," Pignata told the newspaper.
"But the focus, as you would understand, has been on finding a new coach after Ian (Crook) left and getting the club back on track.
"Now we have appointed Frank Farina (as coach). It will be a matter for the board to sit down and sort out something in regards to Ale in the next few weeks".
Sydney have had a miserable season and are currently bottom of the A-League ladder after 10 games, having won just three.