The 38-year-old Italian signed a two-year deal in September but Sydney are willing to offer him an extension now to ward off reported interest from Brazilian side Flamengo.
Del Piero's brother and agent Stefano has arrived in Sydney with talks scheduled for the weekend.
Club chief executive Tony Pignata is optimistic an announcement will be made before next weekend's clash with Melbourne Heart.
"We hope so. These things take a bit of time but we'll do what we can as quickly as possible," said Pignata.
"They're (Del Piero's representatives) here to have a discussion but as I've said before we're very confident of retaining Alessandro for next season.
"There's no doubt there's been interest from other clubs but that's part and parcel of football. We're confident he'll stay."