The flamboyant supremo has confessed that the Giallorossi are interested in acquiring the left-back, and conceded that he will only let the player go if he wants to leave
The Sicilians previously denied that they were in talks with the Stadio Olimpico side to sell the Italy international, but Zamparini has now admitted that the Giallorossi have joined the race for the left-back's signature.
"Aside from Napoli, there's also interest from Rome, and I can tell that it's not Lazio. Roma are interested in signing Balzaretti," Zamparini stated to Radio Radio.
"However, Palermo won't just give the player away. We don't need to sell anyone, but if he wants to leave, we're willing to open talks.
"He has the right characteristics to fit in at Roma. He can do well with his drive and experience, as we've all seen with the national team.
"It depends on the player whether he'll join Napoli or Roma. We'll continue talks this week. If there's no agreement by July 31, Balzaretti won't go anywhere."
The left-back has a contract with Palermo until June 2013.