The Italian striker is the latest name in an ever-decresing list of strikers available to Brendan Rodgers, but Southampton and Celtic have also expressed an interest in the former Juventus star.
"Liverpool have come in - and they're a big club, there's no denying that," said Sydney chief executive Tony Pignata. "But I think the attraction of Australia might sway us.
"We're all anxious. I'm sure there's a lot of fans out there hanging on to get a decision. We've just got to be patient. We've only been in these negotiations for a week and sometimes these sort of negotiations take longer.
"We'll know soon one way or the other."