Rossi, who is currently recovering from a knee operation, has been linked with a return to Serie A for some time.
Roma, Juventus, Napoli and Inter Milan were reportedly keen to acquire the 25-year-old's services before Rossi suffered a recurrence of a cruciate injury in his right knee back in April.
The former Manchester United player is expected to return to play in January 2013.
"Roma had shown an interest in Giuseppe Rossi," Rossi's agent Federico Pastorello told Gazzetta dello Sport.
"However, negotiations have proved more difficult since the player's injury.
"Talks will re-open once Giuseppe returns to play."
Rossi is under contract with Spanish side Villarreal until June 2016. Villarreal were relegated to the Segunda Division last month.
Neymar's move from Santos to Barcelona is no doubt the biggest summer transfer.
Barcelona will wear this new home soccer jersey next season. They also have a new away jersey. Get them both.
The USA will wear their blue away jersey against Jamaica in their World Cup qualifier on Friday night.
Support the USA national team with an official 2013 Centennial soccer jersey from Nike. Its Official.
England will debut their new away jersey against Brazil at the Maracana Stadium on Sunday. Get in the Gear
The hoop soccer jersey is classic and cool. The USA hooped jersey is perfect for every fan. Get in the Gear.
The Nike Hypervenom is the latest cleat silo from Nike. It will change your game and is worn by the game's top players.
Germany is one of the top teams ever and they will play the US on Sunday.
Manchester City will try and win back the Premier League title with this new soccer jersey from Nike!
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.