The 32-year-old former Liverpool and England striker had been in negotiations with the New South Wales club over a possible move to play in the A-League in 2007-08 but he has chosen not to move Down Under.
Sydney FC chief executive officer George Perry said: "Naturally, we're bitterly disappointed but we're satisfied we did everything we could to persuade Robbie to come to Sydney FC, Australia and the Hyundai A-League competition.
"Robbie was tremendously impressed by what he saw in Sydney but he has chosen to go elsewhere. We respect his decision and wish him and his family well."
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