Representative believes a move to Camp Nou would be a dream come true for the Italy international, but revealed that Barca have yet to make an official bid
The 24-year-old has caught the attention of clubs such as Barca, Inter and Juventus with his fine performances for the Yellow Submarine in 2010-11.
While Pastorello stressed that the Italian is keen on a move to Barcelona, he encouraged the Champions League winners to make their intentions known to clarify the situation for all parties.
"It would be a dream for Giuseppe to play for a big club like Barcelona. However, there is nothing concrete at the moment," he was quoted as saying by Premium Calcio.
"It is very important that Barcelona give some sort of a signal of their intentions.
"I think that we can go on to reach an agreement if they make a formal offer for Giuseppe."
Pastorello then revealed that there a number of teams who have made enquiries as to the availability of the former Manchester United striker.
He added: "Several teams have made their interest known. There are also a few Italian sides among the interested outfits."
As well as Rossi, Barcelona have also been heavily linked with a move Udinese star Alexis Sanchez, but the Camp Nou side could opt to focus their attention to the Italian amid strong competition from Manchester City and Inter.