The Phoenix were chasing Rossi in hopes the Italian would be signed under A-League's marquee player rules, the league's incentive to help clubs sign bigger-name international players.
However, Fox Football Executive Producer Murray Shaw revealed that the Nix's pursuit of Rossi has ended.
"I can tell you that they ended, unfortunately, they got deep in discussion with bringing Giuseppe Rossi – the 31-year-old former Italian national team striker down to New Zealand as their marquee for this season," Shaw said on Fox Sports' FootBald podcast.
"[Rossi scored] 32 goals in 52 games for Villarreal back in 2010-11, he was at Manchester United and I think Newcastle United early in his career.
"But unfortunately just got slightly priced out of being a marquee for them, probably due to the fact that the FFA didn't see him as an A class marquee and therefore the Wellington Phoenix didn't quite have enough money to be able to match what they would have got out of the FFA.
However, Phoenix fans can still hope for a marquee signing, as head coach Mark Rudan is still in pursuit of a player to fit the bill.
"What we do know out of all of that, is that the Wellington Phoenix are very much on the lookout for a marquee and things are going well at the Nix under Mark Rudan at this early part of the season," said Shaw.
The Phoenix are unbeaten through their first two matches of the new A-League season, their best start since 2012.
