According to Fairfax media, negotiations fell through after Sydney FC balked at Rossi’s extraordinarily high salary demands.
The 31-year-old former Manchester United, Villarreal and Fiorentina forward then set his sights on Wellington Phoenix, but for similar reasons, a deal could not be reached.
Sydney FC eventually signed English striker Adam le Fondre instead.
Rossi was part of Italy's 2010 World Cup campaign, and was said to be one of the best forwards in La Liga and Serie A.
But his career has been hampered by a string of bad knee injuries, which included rupturing his ACL three times and undergoing “four or five” knee surgeries (he’s lost count).
He has allegedly been injured for a quarter of his 14-year career as a footballer.
Rossi remains without a club since his contract with Genoa Serie A ended last year.