The Italy international has been heavily linked with a return to Juventus, who retain a 50 per cent share in the 25-year-old attacker, and Giovinco admitted on Tuesday that he would be open to rejoining the Bianconeri in the summer.
However, the player's representative, Andrea D'Amico, has now claimed that the Turin giants are facing competition from the Blaugrana for his client's signature.
"The interest of a club like Barcelona is always nice," the agent is quoted as saying by Sportal.it.
"Giovinco is now a major player of great talent and great technique who is now realising his potential, so it's normal that there is interest."
"As for his future? First we must find a solution regarding the ownership between Juventus and Parma. I think this is a necessary step."
D'Amico added that he believes that the race for Giovinco's signature will intensify after Euro 2012.
"He's doing very well and will go to [Poland and Ukraine]," he argued. "As [Italy coach Cesare] Prandelli has said himself, he is one of the biggest talents in Italian football.
"Euro 2012 will be another chance for him to showcase his ability. He is now ready for a big club."
Giovinco, who has been capped seven times by the Azzurri, came through the youth team ranks at Juve before moving to Parma in 2010.
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