The 27-year-old Italian international injured his knee against Livorno in January, but was expected to make a full recovery in time for the showcase event which gets underway in June.
However, Rossi has now turned his attention to short-term goals as he continues his rehabilitation.
"[The World Cup] has been my goal from the beginning of the season, but it's not my goal now," the former Manchester United player is quoted as saying by The New York Times.
"What I'm thinking about now are the short-term goals. I can't think long-term, even a couple of months. I've got to do the small things first. I've got another couple of weeks to rehab."
Rossi made his international debut in 2008, going on to represent the Azzurri 29 times.