Rossi currently plays for Villarreal and the former Manchester United player would jump at the chance to join the Nou Camp side.
Rossi shone for Villarreal last season; hitting 32 goals in the process, helping the club to a fourth place finish in La Liga and clinching a spot in next season's Champions League.
Rossi’s agent Federico Pastorello has revealed interest from a number of European clubs including Champions League winners Barcelona.
Pastorello speaking to Premium Calcio added; "A week before the Champions League final we were told that Rossi was one of three players who they [Barcelona] were thinking about in order to strengthen the side. But things haven't got moving yet and there are no concrete facts at this moment in time,"
He also said; "A lot of European sides are paying attention to Giuseppe and that includes some Italian ones.
"It would be important if there was some sort of signal from Barcelona at a club level to Villarreal. With an official approach I think the deal can be done.
"His dream is to certainly wear the Barcelona shirt, as that represents a winning model."
